Bibliography
- [1]
S.R. Adke and S.M. Manjunath(1984)
An introduction to finite markov processes.
Wiley.
Cited by: 2.9.
- [2]
R.J. Adler and R. Epstein(1987)
Some central limit theorems for Markov paths and some properties of Gaussian random fields.
Stochastic Process. Appl. 24, pp. 157–202.
Cited by: 14.6.2.
- [3]
M. Ajtai, J. Komlós and E. Szemerédi(1983)
Sorting in parallel steps.
Combinatorica 3, pp. 1–19.
Cited by: 10.6.
- [4]
M. Ajtai, J. Komlós and E. Szemerédi(1987)
Deterministic simulation in logspace.
pp. 132–140.
Cited by: 10.4.1,
10.6,
10.6.
- [5]
D.J. Aldous and A. Bandyopadhyay(2001)
How to combine fast heuristic Markov chain Monte Carlo with slow exact sampling.
Note: Unpublished
Cited by: 11.6.2.
- [6]
D.J. Aldous and M. Brown(1992)
Inequalities for rare events in time-reversible Markov chains I.
Lecture Notes, Vol. 22, pp. 1–16.
Cited by: 3.8.
- [7]
D.J. Aldous and P. Diaconis(1986)
Shuffling cards and stopping times.
Amer. Math. Monthly 93, pp. 333–348.
Cited by: 4.7,
9.7.
- [8]
D.J. Aldous and P. Diaconis(1987)
Strong uniform times and finite random walks.
Adv. in Appl. Math. 8, pp. 69–97.
Cited by: 4.7,
7.1.7,
7.4,
9.7.
- [9]
D.J. Aldous and B. Larget(1992)
A tree-based scaling exponent for random cluster models.
J. Phys. A: Math. Gen. 25, pp. L1065–L1069.
Cited by: 9.7.
- [10]
D.J. Aldous, L. Lovász and P. Winkler(1997)
Mixing times for uniformly ergodic Markov chains.
Stochastic Process. Appl. 71, pp. 165–185.
Cited by: 13.4.
- [11]
D.J. Aldous(1982)
Markov chains with almost exponential hitting times.
Stochastic Process. Appl. 13, pp. 305–310.
Cited by: 3.8.
- [12]
D.J. Aldous(1982)
Some inequalities for reversible Markov chains.
J. London Math. Soc. (2) 25, pp. 564–576.
Cited by: 10.9,
4.3.1,
4.3.2,
4.3.2,
4.7,
4.7.
- [13]
D.J. Aldous(1983)
Minimization algorithms and random walk on the d-cube.
Ann. Probab. 11, pp. 403–413.
Cited by: 10.4.2.
- [14]
D.J. Aldous(1983)
On the time taken by random walks on finite groups to visit every state.
Z. Wahrsch. Verw. Gebiete 62, pp. 361–374.
Cited by: 13.4,
7.4.
- [15]
D.J. Aldous(1983)
Random walks on finite groups and rapidly mixing Markov chains.
Seminaire de Probabilites XVII,
pp. 243–297.
Note: Lecture Notes in Math. 986
Cited by: 12.2,
14.8.
- [16]
D.J. Aldous(1987)
On the Markov chain simulation method for uniform combinatorial distributions and simulated annealing.
Probab. Engineering Inform. Sci. 1, pp. 33–46.
Cited by: 4.7,
7.1.8.
- [17]
D.J. Aldous(1988)
Finite-time implications of relaxation times for stochastically monotone processes.
Probab. Th. Rel. Fields 77, pp. 137–145.
Cited by: 4.7,
9.5,
9.5.
- [18]
D.J. Aldous(1989)
Hitting times for random walks on vertex-transitive graphs.
Math. Proc. Cambridge Philos. Soc. 106, pp. 179–191.
Cited by: 3.8,
7.1.4,
7.4.
- [19]
D.J. Aldous(1990)
The random walk construction of uniform spanning trees and uniform labelled trees.
SIAM J. Discrete Math. 3, pp. 450–465.
Cited by: 9.7.
- [20]
D.J. Aldous(1991)
Meeting times for independent Markov chains.
Stochastic Process. Appl. 38, pp. 185–193.
Cited by: 14.2.
- [21]
D.J. Aldous(1991)
Random walk covering of some special trees.
J. Math. Analysis Appl. 157, pp. 271–283.
Cited by: 13.4,
6.6.2,
6.9,
6.27.
- [22]
D.J. Aldous(1991)
The continuum random tree II: an overview.
pp. 23–70.
Cited by: 13.4.
- [23]
D.J. Aldous(1991)
Threshold limits for cover times.
J. Theoretical Probab. 4, pp. 197–211.
Cited by: 6.33.
- [24]
D.J. Aldous(1995)
On simulating a Markov chain stationary distribution when transition probabilities are unknown.
IMA Volumes in Mathematics and its Applications, Vol. 72, pp. 1–9.
Cited by: 9.3.2,
9.3.2.
- [25]
R. Aleliunas(1979)
Random walks, universal traversal sequences, and the complexity of maze traversal.
pp. 218–233.
Cited by: 4.7,
6.1,
6.8.1,
6.8.2,
6.9,
6.34.
- [26]
N. Alon, U. Feige, A. Wigderson and D. Zuckerman(1995)
Derandomized graph products.
Comput. Complexity 5, pp. 60–75.
Cited by: 10.7.3,
3.8.
- [27]
N. Alon and Y. Roichman(1994)
Random Cayley graphs and expanders.
Random Struct. Alg. 5, pp. 271–284.
Cited by: 13.4.
- [28]
N. Alon and J. H. Spencer(1992)
The probabilistic method.
Wiley.
Cited by: 1.1.3,
10.7.2,
6.9.
- [29]
N. Alon(1986)
Eigenvalues and expanders.
Combinatorica 6, pp. 83–96.
Cited by: 10.6,
4.7.
- [30]
V. Anantharam and P. Tsoucas(1989)
A proof of the Markov chain tree theorem.
Stat. Probab. Letters 8, pp. 189–192.
Cited by: 9.7.
- [31]
W.J. Anderson(1991)
Continuous-time Markov chains.
Springer–Verlag.
Cited by: 2.9,
5.4,
5.4.
- [32]
D. Applegate, R. Kannan and N. Polson(1990)
Random polynomial time algorithms for sampling from joint distributions.
Technical report
Carnegie-Mellon.
Cited by: 5.2.
- [33]
D. Applegate and R. Kannan(1991)
Sampling and integration of log-concave functions.
pp. 156–163.
Cited by: 10.6,
5.2.
- [34]
S. Asmussen, P.W. Glynn and H. Thorisson(1992)
Stationarity detection in the initial transient problem.
ACM Trans. Modeling and Computer Sim. 2, pp. 130–157.
Cited by: 9.7.
- [35]
S. Asmussen(1987)
Applied probability and queues.
Wiley.
Cited by: 2.9,
4.7.
- [36]
L. Babai(1991)
Local expansion of vertex-transitive graphs and random generation in finite groups.
pp. 164–174.
Cited by: 10.7.3,
3.8,
7.1.8.
- [37]
L. Babai(1994)
Probably true theorems, cry wolf?.
Notices Amer. Math. Soc. 41, pp. 453–454.
Cited by: 10.3.1.
- [38]
P. Baldi and Y. Rinott(1989)
Asymptotic normality of some graph-related statistics.
J. Appl. Probab. 26, pp. 171–175.
Cited by: 14.8.
- [39]
C. Bandle(1980)
Isoperimetric inequalities and applications.
Pitman, Boston MA.
Cited by: 4.4.3.
- [40]
M.T. Barlow(1991)
Random walks and diffusions on fractals.
pp. 1025–1035.
Cited by: 13.4.
- [41]
M.T. Barlow(1998)
Diffusions on fractals.
Lecture Notes in Math., Vol. 1690.
Cited by: 13.4.
- [42]
G. Barnes and U. Feige(1996)
Short random walks on graphs.
SIAM J. Discrete Math. 9, pp. 19–28.
Cited by: 6.9.
- [43]
M.F. Barnsley and J.H. Elton(1988)
A new class of Markov processes for image encoding.
Adv. in Appl. Probab. 20, pp. 14–32.
Cited by: 9.7.
- [44]
J.R. Baxter and R.V. Chacon(1976)
Stopping times for recurrent Markov processes.
Illinois J. Math. 20, pp. 467–475.
Cited by: 2.10.1.
- [45]
K.A. Berman and M. Konsowa(1990)
Random paths, electrical networks and reversible Markov chains.
SIAM J. Discrete Math. 3, pp. 311–319.
Cited by: 3.8.
- [46]
J. Besag and P.J. Greene(1993)
Spatial statistics and Bayesian computation.
J. Royal Statist. Soc. (B) 55, pp. 25–37.
Note: Followed by discussion
Cited by: 11.7.
- [47]
S. Bhatt and J. Cai(1993)
Taking random walks to grow trees in hypercubes.
J. Assoc. Comput. Mach. 40, pp. 741–764.
Cited by: 10.4.3,
10.4.3.
- [48]
N. L. Biggs(1974)
Algebraic graph theory.
Cambridge University Press.
Cited by: 7.4,
7.
- [49]
N. L. Biggs(1993)
Potential theory on distance-regular graphs.
Combin. Probab. Comput. 2, pp. 243–255.
Cited by: 7.3.4,
7.3.
- [50]
L.J. Billera and P. Diaconis(2000)
A geometric interpretation of the Metropolis algorithm.
Note: Unpublished
Cited by: 11.7.
- [51]
N. H. Bingham(1991)
Fluctuation theory for the Ehrenfest urn.
Adv. in Appl. Probab. 23, pp. 598–611.
Cited by: 5.4,
5.4,
5.4.
- [52]
D. Boivin(1993)
Weak convergence for reversible random walks in a random environment.
Ann. Probab. 21, pp. 1427–1440.
Cited by: 13.3.6.
- [53]
B. Bollobás(1985)
Random graphs.
Academic Press, London.
Cited by: 9.3.1.
- [54]
B. Bollobás(1988)
The isoperimetric number of random regular graphs.
European J. Combin. 9, pp. 241–244.
Cited by: 13.4.
- [55]
E. Bolthausen(1980)
The Berry-Esseen theorem for functionals of discrete Markov chains.
Z. Wahrsch. Verw. Gebiete 54, pp. 59–73.
Cited by: 4.7.
- [56]
A. Borodin, W.L. Ruzzo and M. Tompa(1992)
Lower bounds on the length of universal traversal sequences.
J. Computer Systems Sci. 45, pp. 180–203.
Cited by: 6.9.
- [57]
K. Borre and P. Meissl(1974)
Strength analysis of leveling-type networks.
Geodaetisk Institut, Copenhagen.
Note: Volume 50
Cited by: 3.7.1,
3.8.
- [58]
O. Bottema(1935)
Uber die Irrfahrt in einem Strassennetz.
Math. Z. 39, pp. 137–145.
Cited by: 3.8.
- [59]
R.C. Bradley, W. Bryc and S. Janson(1987)
On dominations between measures of dependence.
J. Multivariate Anal. 23, pp. 312–329.
Cited by: 4.7.
- [60]
L.A. Breyer and G.O. Roberts(1998)
From Metropolis to diffusions: Gibbs states and optimal scaling.
Technical report
Statistical Lab., Cambridge U.K..
Cited by: 11.7.
- [61]
G. Brightwell and P. Winkler(1990)
Extremal cover times for random walks on trees.
J. Graph Theory 14, pp. 547–554.
Cited by: 6.7.
- [62]
G. Brightwell and P. Winkler(1990)
Maximum hitting time for random walks on graphs.
Random Struct. Alg. 1, pp. 263–276.
Cited by: 6.11.
- [63]
P.J. Brockwell and R.A. Davis(1987)
Time series: theory and methods.
Springer–Verlag.
Cited by: 11.7.
- [64]
A. Broder, A.R. Karlin, P. Raghavan and E. Upfal(1989)
Trading space for time in undirected connectivity.
pp. 543–549.
Cited by: 6.4.1,
6.8.2,
6.9.
- [65]
A. Broder and A.R. Karlin(1989)
Bounds on the cover time.
J. Theoretical Probab. 2, pp. 101–120.
Cited by: 3.8,
3.8,
6.9.
- [66]
A. Broder and E. Shamir(1987)
On the second eigenvalue of random regular graphs.
pp. 286–294.
Cited by: 13.4.
- [67]
A. Z. Broder, A. M. Frieze and E. Upfal(1994)
Existence and construction of edge disjoint paths on expander graphs.
SIAM J. Comput. 23, pp. 976–989.
Cited by: 10.2.2.
- [68]
A. Z. Broder, A. M. Frieze and E. Upfal(1999)
Static and dynamic path selection on expander graphs: a random walk approach.
Random Struct. Alg. 14, pp. 87–109.
Cited by: 10.6.
- [69]
A. Broder(1986)
How hard is it to marry at random? (on the approximation of the permanent).
pp. 50–58.
Cited by: 10.5.2.
- [70]
A. Broder(1989)
Generating random spanning trees.
pp. 442–447.
Cited by: 9.7.
- [71]
A.E. Brouwer, A.M. Cohen and A. Neumaier(1989)
Distance regular graphs.
Springer–Verlag.
Cited by: 7.2.4,
7.3.4,
7.3,
7.3,
7.4.
- [72]
M. Brown(1983)
Approximating IMRL distributions by exponential distributions, with applications to first passage times.
Ann. Probab. 11, pp. 419–427.
Cited by: 3.5.4,
3.8.
- [73]
M. Brown(1990)
Consequences of monotonicity for Markov transition functions.
Technical report
City College, CUNY.
Cited by: 3.8,
3.8,
9.7.
- [74]
M. Brown(1999)
Interlacing eigenvalues in time reversible Markov chains.
Math. Oper. Res. 24, pp. 847–864.
Cited by: 3.8.
- [75]
M.J.A.M. Brummelhuis and H.J. Hilhorst(1991)
Covering of a finite lattice by a random walk.
Physica A 176, pp. 387–408.
Cited by: 7.4.
- [76]
D. Brydges, S.N. Evans and J.Z. Imbrie(1992)
Self-avoiding walk on a hierarchical lattice in four dimensions.
Ann. Probab. 20, pp. 82–124.
Cited by: 13.4.
- [77]
R. Bubley, M. Dyer and C. Greenhill(1998)
Beating the bound for approximately counting colorings: a computer-assisted proof of rapid mixing.
New York, pp. 355–363.
Cited by: 12.1.12,
12.2.
- [78]
R. Bubley, M. Dyer and M. Jerrum(1998)
An elementary analysis of a procedure for sampling points in a convex body.
Random Struct. Alg. 12, pp. 213–235.
Cited by: 10.5.1,
11.6.1,
13.1.3.
- [79]
R. Bubley and M. Dyer(1997)
Path coupling: a technique for proving rapid mixing in Markov chains.
pp. 223–231.
Cited by: 12.1.12.
- [80]
R. Bubley and M. Dyer(1999)
Faster random generation of linear extensions.
Discrete Math. 201, pp. 81–88.
Cited by: 12.1.13.
- [81]
F. Buckley and F. Harary(1990)
Distance in graphs.
Addison-Wesley.
Cited by: 5.3.1.
- [82]
K. Burdzy and W.S. Kendall(2000)
Efficient Markovian couplings: examples and counterexamples.
Ann. Appl. Probab. 10, pp. 362–409.
Cited by: 13.4.
- [83]
R. Burton and R. Pemantle(1993)
Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances.
Ann. Probab. 21, pp. 1329–1371.
Cited by: 9.7,
9.7.
- [84]
E.A. Carlen, S. Kusuoka and D.W. Stroock(1987)
Upper bounds for symmetric Markov transition functions.
Ann. Inst. H. Poincaré Probab. Statist. Suppl. 2, pp. 245–287.
Cited by: 6.9.
- [85]
A.K. Chandra, P. Raghavan, W.L. Ruzzo, R. Smolensky and P. Tiwari(1996/7)
The electrical resistance of a graph captures its commute and cover times.
Comput. Complexity 6, pp. 312–340.
Note: Extended abstract originally published in
Proc. 21st ACM Symp. Theory of Computing (1989) 574-586
Cited by: 10.6,
13.2.3,
3.3.3,
3.8,
6.9.
- [86]
G. Chartrand and L. Lesniak(1986)
Graphs and digraphs.
2nd edition, Wadsworth, Monterey CA.
Cited by: 4.1,
6.5.1.
- [87]
J. Cheeger(1970)
A lower bound for the lowest eigenvalue for the Laplacian.
pp. 195–199.
Cited by: 4.7.
- [88]
M. F. Chen(1992)
From Markov chains to non-equilibrium particle systems.
World Scientific, Singapore.
Cited by: 1.2.3,
3.8,
3.8.
- [89]
M. F. Chen(1996)
Trilogy of couplings and general formulas for lower bound of spectral gap.
Lecture Notes in Statistics, pp. 123–136.
Cited by: 13.4.
- [90]
M. F. Chen(1999)
Eigenvalues, inequalities and ergodic theory II.
Adv. Math. (China) 28, pp. 481–505.
Cited by: 13.4.
- [91]
M.-H. Chen, Q.-M. Shao and J.G. Ibrahim(2000)
Monte carlo methods in bayesian computation.
Springer–Verlag.
Cited by: 11.7.
- [92]
F.R.K. Chung, P. Diaconis and R. L. Graham(1987)
A random walk problem arising in random number generation.
Ann. Probab. 15, pp. 1148–1165.
Cited by: 7.4.
- [93]
F.R.K. Chung and S.-T. Yau(1995)
Eigenvalues of graphs and Sobolev inequalities.
Combin. Probab. Comput. 4, pp. 11–25.
Cited by: 3.8.
- [94]
F.R.K. Chung(1979)
On concentrators, superconcentrators, and nonblocking networks.
Bell System Tech. J. 58, pp. 1765–1777.
Cited by: 13.4.
- [95]
F.R.K. Chung(1997)
Spectral graph theory.
CBMS Regional Conference Series in Mathematics, Vol. 92, Amer. Math. Soc..
Cited by: 1.2.3,
10.1.1,
10.2,
10.6,
10.6,
10.6.
- [96]
K.L. Chung(1967)
Markov chains with stationary transition probabilities.
Second edition, Springer–Verlag.
Cited by: 2.9.
- [97]
A. Cohen and A. Widgerson(1989)
Dispensers, deterministic amplification, and weak random sources.
pp. 14–19.
Cited by: 10.6.
- [98]
A. Condon and D. Hernek(1994)
Random walks on colored graphs.
Random Struct. Alg. 5, pp. 285–303.
Cited by: 6.9.
- [99]
D. Coppersmith, P. Doyle, P. Raghavan and M. Snir(1993)
Random walks on weighted graphs and applications to on-line algorithms.
J. Assoc. Comput. Mach. 40, pp. 421–453.
Cited by: 10.4.4,
10.10,
3.8,
3.8.
- [100]
D. Coppersmith, U. Feige and J. Shearer(1996)
Random walks on regular and irregular graphs.
SIAM J. Discrete Math. 9, pp. 301–308.
Cited by: 6.9,
6.9.
- [101]
D. Coppersmith, P. Tetali and P. Winkler(1993)
Collisions among random walks on a graph.
SIAM J. Discrete Math. 6, pp. 363–374.
Cited by: 3.1.1,
3.8.
- [102]
M.K. Cowles and B.P. Carlin(1996)
Markov chain Monte Carlo convergence diagnostics: a comparative review.
J. Amer. Statist. Assoc. 91, pp. 883–904.
Cited by: 11.7.
- [103]
J.T. Cox and D. Griffeath(1990)
Mean field asymptotics for the planar stepping stone model.
Proc. London Math. Soc. 61, pp. 189–208.
Cited by: 14.8.
- [104]
J.T. Cox(1989)
Coalescing random walks and voter model consensus times on the torus in .
Ann. Probab. 17, pp. 1333–1366.
Cited by: 14.3.3,
14.3.5.
- [105]
S. L. Cuéllar-Montoya(1997)
A rapidly mixing stochastic system of finite interacting particles on the circle.
Stochastic Process. Appl. 67, pp. 69–99.
Cited by: 14.7.
- [106]
D.M. Cvetkovic, M. Doob, I. Gutman and A. Torgasev(1988)
Recent results in the theory of graph spectra.
North-Holland.
Note: Annals of Discrete Math. 36
Cited by: 10.6.
- [107]
D.M. Cvetkovic, M. Doob and H. Sachs(1980)
Spectra of graphs.
Academic Press.
Cited by: 10.6,
3.8.
- [108]
C. Dellacherie and P.-A. Meyer(1983)
Probabilités et potentiel: théorie discrète du potentiel.
Hermann, Paris.
Cited by: 9.7.
- [109]
L. Devroye and A. Sbihi(1990)
Random walks on highly-symmetric graphs.
J. Theoretical Probab. 3, pp. 497–514.
Cited by: 7.3.2,
7.4.
- [110]
L. Devroye and A. Sbihi(1992)
Inequalities for random walks on trees.
Vol. 2, pp. 35–45.
Cited by: 6.9.
- [111]
L. Devroye(1986)
Nonuniform random number generation.
Springer–Verlag.
Cited by: 11.7.
- [112]
P. Diaconis and J.A. Fill(1990)
Examples for the theory of strong stationary duality with countable state spaces.
Prob. Engineering Inform. Sci. 4, pp. 157–180.
Cited by: 4.7,
9.7.
- [113]
P. Diaconis and J.A. Fill(1990)
Strong stationary times via a new form of duality.
Ann. Probab. 18, pp. 1483–1522.
Cited by: 4.7,
5.1.3,
9.7.
- [114]
P. Diaconis, R.L. Graham and J.A. Morrison(1990)
Asymptotic analysis of a random walk on a hypercube with many dimensions.
Random Struct. Alg. 1, pp. 51–72.
Cited by: 5.2.
- [115]
P. Diaconis and L. Saloff-Coste(1993)
Comparison theorems for random walk on finite groups.
Ann. Probab. 21, pp. 2131–2156.
Cited by: 14.5.1,
14.8,
7.1.9,
7.2.1,
7.4,
8.1,
8.1,
8.3,
8.
- [116]
P. Diaconis and L. Saloff-Coste(1993)
Comparison theorems for reversible Markov chains.
Ann. Appl. Probab. 3, pp. 696–730.
Cited by: 8.1,
8.1,
8.1,
8.1,
8.
- [117]
P. Diaconis and L. Saloff-Coste(1996)
Logarithmic Sobolev inequalities for finite Markov chains.
Ann. Appl. Probab. 6, pp. 695–750.
Cited by: 8.4.1,
8.4.2,
8.4.2,
8.4.3,
8.4.3,
8.4,
8.
- [118]
P. Diaconis and L. Saloff-Coste(1996)
Nash inequalities for finite Markov chains.
J. Theoretical Probab. 9, pp. 459–510.
Cited by: 8.2.3,
8.
- [119]
P. Diaconis and L. Saloff-Coste(1998)
What do we know about the Metropolis algorithm?.
J. Comput. System Sci. 57, pp. 20–36.
Cited by: 11.7.
- [120]
P. Diaconis and M. Shahshahani(1981)
Generating a random permutation with random transpositions.
Z. Wahrsch. Verw. Gebiete 57, pp. 159–179.
Cited by: 7.2.1,
8.9.
- [121]
P. Diaconis and M. Shahshahani(1986)
Time to reach stationarity in the Bernouilli-Laplace diffusion model.
SIAM J. Math. Anal. 18, pp. 208–218.
Cited by: 7.3.2.
- [122]
P. Diaconis and D. Stroock(1991)
Geometric bounds for eigenvalues of Markov chains.
Ann. Appl. Probab. 1, pp. 36–61.
Cited by: 3.8,
4.4.3,
4.4.3,
4.5.2,
4.7.
- [123]
P. Diaconis(1988)
Group representations in probability and statistics.
Institute of Mathematical Statistics, Hayward CA.
Cited by: 1.2.3,
5.2,
5.2,
7.2.1,
7.3.2,
7.3.5,
7.4,
7,
8.9,
9.1.3.
- [124]
P. Diaconis(1996)
Notes on the hit-and-run algorithm.
Note: Unpublished
Cited by: 11.2.2.
- [125]
I.H. Dinwoodie(1995)
A probability inequality for the occupation measure of a reversible Markov chain.
Ann. Appl. Probab. 5, pp. 37–43.
Cited by: 10.7.1.
- [126]
W. Doeblin(1938)
Exposé de la theorie des chaînes simples constantes de Markov à un nombre fini d’états.
Rev. Math. Union Interbalkanique 2, pp. 77–105.
Cited by: 12.2.
- [127]
P. Donnelly, P. Lloyd and A. Sudbury(1994)
Approach to stationarity of the Bernouilli-Laplace diffusion model.
Adv. in Appl. Probab. 26, pp. 715–727.
Cited by: 7.3.2.
- [128]
P. Donnelly and D. Welsh(1983)
Finite particle systems and infection models.
Math. Proc. Cambridge Philos. Soc. 94, pp. 167–182.
Cited by: 14.8.
- [129]
P. Donnelly and D. Welsh(1984)
The antivoter problem: random -colourings of graphs.
pp. 133–144.
Cited by: 14.4,
14.4,
14.8.
- [130]
C. Dou and M. Hildebrand(1996)
Enumeration and random random walks on finite groups.
Ann. Probab. 24, pp. 987–1000.
Cited by: 13.4.
- [131]
P.G. Doyle and J.L. Snell(1984)
Random walks and electrical networks.
Mathematical Association of America, Washington DC.
Cited by: 1.2.3,
13.2.2,
3.3.3,
3.7.1,
3.8,
3.8.
- [132]
R. Durrett(1988)
Lecture notes on particle systems and percolation.
Wadsworth, Pacific Grove CA.
Cited by: 14.3.3,
14.8,
14.
- [133]
R. Durrett(1991)
Probability: theory and examples.
Wadsworth, Pacific Grove CA.
Cited by: 1.2.2,
1.2.3,
13.1.1,
13.1.1,
13.1.4,
13.1.6,
13.2.1,
13.2.2,
13.2.4,
13.4,
2.3,
2.3,
2.5.3,
2.8.1,
2.8.3,
2.9,
2.9,
3.5.3,
3.7,
4.7,
4.7,
6.2,
7.4.
- [134]
M. Dyer, A. Frieze and R. Kannan(1989)
A random polynomial time algorithm for approximating the volume of convex bodies.
pp. 375–381.
Cited by: 10.5.1.
- [135]
M. Dyer, A. Frieze and R. Kannan(1991)
A random polynomial time algorithm for approximating the volume of convex bodies.
J. Assoc. Computing Machinery 38, pp. 1–17.
Cited by: 10.5.1.
- [136]
M. Dyer and A. Frieze(1991)
Computing the volume of convex bodies: a case where randomness provably helps.
Proc. Symp. Applied Math., Vol. 44, pp. 123–170.
Cited by: 10.6.
- [137]
M. Dyer and C. Greenhill(1998)
A genuinely polynomial-time algorithm for sampling two-rowed contingency tables.
Technical report
University of Leeds, U.K..
Note: Unpublished
Cited by: 12.2.
- [138]
M.L. Eaton(1997)
Admissability in quadratically regular problems and recurrence of symmetric Markov chains: why the connection?.
J. Statist. Plann. Inference 64, pp. 231–247.
Cited by: 13.4.
- [139]
R.G. Edwards and A.D. Sokal(1988)
Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm.
Phys. Rev. D 38, pp. 2009–2012.
Cited by: 11.7.
- [140]
B. Efron and C. Stein(1981)
The jackknife estimate of variance.
Ann. Statist. 10, pp. 586–596.
Cited by: 4.7.
- [141]
S.N. Ethier and T. G. Kurtz(1986)
Markov processes: characterization and convergence.
Wiley, New York.
Cited by: 13.1.1.
- [142]
U. Feige(1995)
A tight lower bound on the cover time for random walks on graphs.
Random Struct. Alg. 6, pp. 433–438.
Cited by: 6.6.4.
- [143]
U. Feige(1995)
A tight upper bound on the cover time for random walks on graphs.
Random Struct. Alg. 6.
Cited by: 6.12.
- [144]
U. Feige(1996/7)
Collecting coupons on trees, and the cover time of random walks.
Comput. Complexity 6, pp. 341–356.
Cited by: 6.12,
6.15.
- [145]
W. Feller(1971)
An introduction to probability theory and its applications.
2nd edition, Vol. II, Wiley.
Cited by: 14.6.2.
- [146]
M. Fiedler, C.R. Johnson, T.L. Markham and M. Neumann(1985)
A trace inequality for -matrices and the symmetrizability of a real matrix by a positive diagonal matrix.
Linear Alg. Appl. 71, pp. 81–94.
Cited by: 9.4.2,
9.4.2.
- [147]
M. Fiedler(1972)
Bounds for eigenvalues of doubly stochastic matrices.
Linear Algebra Appl. 5, pp. 299–310.
Cited by: 4.7.
- [148]
J. A. Fill and R. Pemantle(1993)
Percolation, first-passage percolation and covering times for Richardson’s model on the -cube.
Ann. Appl. Probab. 3, pp. 593–629.
Cited by: 14.8.
- [149]
J.A. Fill(1991)
Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process.
Ann. Appl. Probab. 1, pp. 62–87.
Cited by: 8.1.
- [150]
J.A. Fill(1991)
Time to stationarity for a continuous-time Markov chain.
Prob. Engineering Inform. Sci. 5, pp. 45–70.
Cited by: 4.7,
9.7.
- [151]
J.A. Fill(1992)
Strong stationary duality for continuous-time Markov chains. part I: theory.
J. Theoretical Probab. 5, pp. 45–70.
Cited by: 4.7,
9.7.
- [152]
L. Flatto, A.M. Odlyzko and D.B. Wales(1985)
Random shuffles and group representations.
Ann. Probab. 13, pp. 154–178.
Cited by: 6.9,
7.2.1.
- [153]
R.M. Foster(1949)
The average impedance of an electrical network.
Ann Arbor, MI, pp. 333–340.
Cited by: 3.3.4.
- [154]
D. Freedman(1983)
Markov chains.
Springer–Verlag.
Note: Reprint of 1971 Holden-Day edition
Cited by: 2.9.
- [155]
J. Friedman, J. Kahn and E. Szemeredi(1989)
On the second eigenvalue in random regular graphs.
pp. 587–598.
Cited by: 13.4.
- [156]
J. Friedman(1991)
On the second eigenvalue and random walk in random regular graphs.
Combinatorica 11, pp. 331–362.
Cited by: 13.4.
- [157]
J. Friedman (Ed.)(1993)
Expanding graphs.
Amer. Math. Soc..
Note: DIMACS volume 10
Cited by: 10.1.1,
10.6.
- [158]
A. Frieze, R. Kannan and N. Polson(1994)
Sampling from log-concave distributions.
Ann. Appl. Probab. 4, pp. 812–837.
Cited by: 10.6,
4.7.
- [159]
M. Fukushima(1980)
Dirichlet forms and Markov processes.
North-Holland.
Cited by: 3.8.
- [160]
A. Gelman, G.O. Roberts and W.R. Gilks(1996)
Efficient Metropolis jumping rules.
Vol. 5, pp. 599–608.
Cited by: 11.7.
- [161]
A. Gelman and D.B. Rubin(1992)
Inference from iterative simulation using multiple sequences.
Statistical Science 7, pp. 457–472.
Note: With discussion
Cited by: 11.7.
- [162]
S. Geman and D. Geman(1984)
Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.
IEEE Trans. Pattern Anal. Mach. Intell. 6, pp. 721–741.
Cited by: 11.7.
- [163]
C.J. Geyer(1991)
Markov chain Monte Carlo maximum likelihood.
pp. 156–163.
Cited by: 11.3.3.
- [164]
A. Giacometti(1995)
Exact closed form of the return probability on the Bethe lattice.
J. Phys. A: Math. Gen. 28, pp. L13–L17.
Cited by: 13.2.7.
- [165]
W.R. Gilks, S. Richardson and D.J. Spiegelhalter (Eds.)(1996)
Markov chain Monte Carlo in practice.
Chapman and Hall, London.
Cited by: 11.7.
- [166]
W.R. Gilks, G.O. Roberts and E.I. George(1994)
Adaptive direction sampling.
The Statistician 43, pp. 179–189.
Cited by: 11.3.4.
- [167]
D. Gillman(1998)
A Chernoff bound for random walks on expander graphs.
SIAM J. Comput. 27, pp. 1203–1220.
Cited by: 10.7.1.
- [168]
F. Gobel and A.A. Jagers(1974)
Random walks on graphs.
Stochastic Process. Appl. 2, pp. 311–336.
Cited by: 3.8,
7.4.
- [169]
S. Golstein(1979)
Maximal coupling.
Z. Wahrsch. Verw. Gebiete 46, pp. 193–204.
Cited by: 9.7.
- [170]
J. Goodman and A. Sokal(1989)
Multigrid Monte Carlo method: conceptual foundations.
Phys. Rev. D 40, pp. 2037–2071.
Cited by: 11.7.
- [171]
D. Griffeath and T. M. Liggett(1982)
Critical phenomena for Spitzer’s reversible nearest particle systems.
Ann. Probab. 10, pp. 881–895.
Cited by: 3.8.
- [172]
D. Griffeath(1974-75)
A maximal coupling for Markov chains.
Z. Wahrsch. Verw. Gebiete, pp. 95–106.
Cited by: 12.2.
- [173]
D. Griffeath(1979)
Additive and cancellative interacting particle systems.
Lecture Notes in Math., Vol. 724, Springer–Verlag.
Cited by: 14.4,
14.
- [174]
P. Griffin(1990)
Accelerating beyond the third dimension: returning to the origin in a simple random walk.
Mathematical Scientist 15, pp. 24–35.
Cited by: 13.2.4.
- [175]
G. Grimmett and H. Kesten(1984)
Random electrical networks on complete graphs.
J. London Math. Soc. (2) 30, pp. 171–192.
Cited by: 13.3.5,
13.4.
- [176]
G. Grimmett and D. Stirzaker(1982)
Probability and random processes.
Oxford University Press.
Cited by: 2.9.
- [177]
G. Grimmett(1993)
Random graphical networks.
Networks and Chaos — Statistical and Probabilistic
Aspects,
pp. 288–301.
Note: Monogr. Statist. Appl. Prob. 50
Cited by: 13.4.
- [178]
H. Haken(1978)
Synergetics.
Springer-Verlag.
Cited by: 9.7.
- [179]
T. Hara and G. Slade(1992)
The number and size of branched polymers in high dimensions.
J. Statist. Phys. 67, pp. 1009–1038.
Cited by: 6.2.
- [180]
W.K. Hastings(1970)
Monte Carlo sampling methods using Markov chains and their applications.
Biometrika 57, pp. 97–109.
Cited by: 11.7.
- [181]
R. Holley and D. Stroock(1987)
Logarithmic Sobolev inequalitites and stochastic Ising models.
J. Statist. Phys. 46, pp. 1159–1194.
Cited by: 8.4.5.
- [182]
D.F. Holt(1981)
A graph which is edge-transitive but not arc-transitive.
J. Graph Theory 5, pp. 201–204.
Cited by: 7.4.
- [183]
R.A. Horn and C.R. Johnson(1985)
Matrix analysis.
Cambridge University Press.
Cited by: 3.4,
3.6.3,
3.6.5,
8.1.
- [184]
B.D. Hughes(1995)
Random walks and random environments.
Oxford University Press.
Cited by: 13.2.4,
13.3.6.
- [185]
K. Hukushima and K. Nemoto(1996)
Exchange Monte Carlo method and application to spin glass simulations.
J. Physics Soc. Japan 65, pp. 1604–1608.
Cited by: 11.3.3.
- [186]
J.J. Hunter(1983)
Mathematical techniques of applied probability.
Academic Press.
Cited by: 1.2.3,
2.10.2,
2.9,
2.9.
- [187]
J.-P. Imhof(1985)
On Brownian bridge and excursion.
Studia Sci. Math. Hungar. 20, pp. 1–10.
Cited by: 6.9.
- [188]
R. Impagliazzo and D. Zuckerman(1989)
How to recycle random bits.
pp. 248–253.
Cited by: 10.4.1,
10.6.
- [189]
M. Iosifescu(1980)
Finite markov processes and their applications.
Wiley.
Cited by: 2.9.
- [190]
R. Isaacs(1965)
Differential games.
Wiley.
Cited by: 4.7.
- [191]
D. Isaacson and R. Madsen(1976)
Markov chains: theory and applications.
Wiley.
Cited by: 2.9.
- [192]
I. Iscoe, D. McDonald and K. Qian(1993)
Capacity of ATM switches.
Ann. Appl. Probab. 3, pp. 277–295.
Cited by: 3.8.
- [193]
I. Iscoe and D. McDonald(1994)
Asymptotics of exit times for Markov jump processes I.
Ann. Probab. 22, pp. 372–397.
Cited by: 3.8.
- [194]
S. Janson(1997)
Gaussian hilbert spaces.
Cambridge Tracts in Mathematics, Cambridge University Press.
Cited by: 2.9,
3.8.
- [195]
E. Janvresse(2001)
Spectral gap for Kac’s model of the Boltzmann equation.
Ann. Probab. 29, pp. 288–304.
Cited by: 13.4.
- [196]
M. Jerrum and A. Sinclair(1989)
Approximating the permanent.
SIAM J. Computing 18, pp. 1149–1178.
Cited by: 10.6.
- [197]
M. Jerrum and A. Sinclair(1996)
The Markov chain Monte Carlo method: an approach to approximate counting and integration.
Boston MA, pp. 482–520.
Cited by: 10.5.2,
10.6.
- [198]
M. Jerrum(1993)
Uniform sampling modulo a group of symmetries using Markov chain simulation.
pp. 37–48.
Note: DIMACS, volume 10
Cited by: 12.2,
14.7.
- [199]
M. Jerrum(1998)
Mathematical foundations of the Markov chain Monte Carlo method.
Algorithms and Combinatorics, pp. 116–165.
Cited by: 10.5.2,
10.6.
- [200]
M.R. Jerrum, L.G. Valiant and V.V. Vazirani(1986)
Random generation of combinatorial structures from a uniform distribution.
Theor. Computer Sci. 43, pp. 169–188.
Cited by: 10.6.
- [201]
M.R. Jerrum(1995)
A very simple algorithm for estimating the number of -colorings of a low-degree graph.
Random Struct. Alg. 7, pp. 157–165.
Cited by: 12.2.
- [202]
C.D. M. Jr.(1975)
The role of the group generalized inverse in the theory of finite Markov chains.
SIAM Review 17, pp. 443–464.
Cited by: 2.9.
- [203]
N. Kahale(1995)
Eigenvalues and expansion of regular graphs.
J. ACM 42, pp. 1091–1106.
Cited by: 3.8.
- [204]
N. Kahale(1997)
Large deviation bounds for Markov chains.
Combin. Probab. Comput. 6, pp. 465–474.
Cited by: 10.7.1.
- [205]
J.D. Kahn, N. Linial, N. Nisan and M.E. Saks(1989)
On the cover time of random walks on graphs.
J. Theoretical Probab. 2, pp. 121–128.
Cited by: 6.1.
- [206]
R. Kannan, L. Lovász and M. Simonovits(1997)
Random walks and an volume algorithm for convex bodies.
Random Struct. Alg. 11, pp. 1–50.
Cited by: 10.5.1.
- [207]
S. Karlin, B. Lindquist and Y. Yao(1993)
Markov chains on hypercubes: spectral representations and several majorization relations.
Random Struct. Alg. 4, pp. 1–36.
Cited by: 7.4.
- [208]
S. Karlin and H.M. Taylor(1975)
A first course in stochastic processes.
Second edition, Academic Press.
Cited by: 13.1.1,
2.8.1,
2.9,
5.1.2.
- [209]
S. Karlin and H.M. Taylor(1981)
A second course in stochastic processes.
Academic Press.
Cited by: 13.4,
2.9,
5.1.3.
- [210]
R.M. Karp, M. Luby and N. Madras(1989)
Monte Carlo approximation algorithms for enumeration problems.
J. Algorithms 10, pp. 429–448.
Cited by: 10.6.
- [211]
A. Karzanov and L. Khachiyan(1991)
On the conductance of order Markov chains.
Order 8, pp. 7–15.
Cited by: 12.2.
- [212]
J. Keilson(1979)
Markov chain models - rarity and exponentiality.
Springer–Verlag.
Cited by: 1.2.3,
3.8,
3.8,
7.4.
- [213]
F.P. Kelly(1979)
Reversibility and stochastic networks.
Wiley.
Cited by: 1.2.3,
2.9,
3.8,
3.8,
3.8.
- [214]
J.G. Kemeny, J. Snell and A.W. Knapp(1976)
Denumerable markov chains.
2nd edition, Springer–Verlag.
Cited by: 2.9,
3.8.
- [215]
J.G. Kemeny and J.L. Snell(1960)
Finite markov chains.
Van Nostrand.
Cited by: 1.2.3,
2.10.2,
2.9,
2.9,
2.9,
2.9.
- [216]
J.H.B. Kemperman(1961)
The passage problem for a stationary markov chain.
University of Chicago Press.
Cited by: 5.4,
5.4.
- [217]
C. Kipnis and S.R.S. Varadhan(1986)
Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions.
Comm. Math. Phys. 104, pp. 1–19.
Cited by: 13.4.
- [218]
W.B. Krebs(1995)
Brownian motion on the continuum tree.
Probab. Th. Rel. Fields 101, pp. 421–433.
Cited by: 13.4.
- [219]
J.C. Lagarias and A. Weiss(1992)
The problem: two stochastic models.
Ann. Appl. Probab. 2, pp. 229–261.
Cited by: 6.2.
- [220]
H.J. Landau and A.M. Odlyzko(1981)
Bounds for eigenvalues of certain stochastic matrices.
Linear Algebra Appl. 38, pp. 5–15.
Cited by: 5.4.
- [221]
L. Lange and J.W. Miller(1992)
A random ladder game: permutations, eigenvalues, and convergence of markov chains.
College Math. Journal 23, pp. 373–385.
Cited by: 14.8.
- [222]
G. Lawler(1993)
On the covering time of a disc by simple random walk in two dimensions.
Seminar in Stochastic Processes 1992,
pp. 189–208.
Cited by: 7.2.2,
7.4.
- [223]
G.F. Lawler and A.D. Sokal(1988)
Bounds on the spectrum for Markov chains and Markov proceses.
Trans. Amer. Math. Soc. 309, pp. 557–580.
Cited by: 4.7.
- [224]
T. Leighton and S. Rao(1988)
An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms.
pp. 422–431.
Cited by: 4.7.
- [225]
G. Letac and L. Takács(1980)
Random walks on a 600-cell.
SIAM J. Alg. Discrete Math. 1, pp. 114–120.
Cited by: 7.3.2.
- [226]
G. Letac and L. Takács(1980)
Random walks on a dodecahedron.
J. Appl. Probab. 17, pp. 373–384.
Cited by: 7.3.2.
- [227]
G. Letac(1981)
Problemes classiques de probabilite sur un couple de Gelfand.
Analytic Methods in Probability Theory,
Note: Lecture Notes in Math. 861
Cited by: 7.3.5.
- [228]
G. Letac(1982)
Les fonctions spheriques d’un couple de Gelfand symmetrique et les chaines de Markov.
Adv. in Appl. Probab. 14, pp. 272–294.
Cited by: 7.3.5.
- [229]
G. Letac(1986)
A contraction principle for certain Markov chains and its applications.
Random Matrices and Their Applications,
Contemp. Math., Vol. 50, pp. 263–273.
Cited by: 9.7.
- [230]
P. Lezaud(1998)
Chernoff-type bound for finite Markov chains.
Ann. Appl. Probab. 8, pp. 849–867.
Cited by: 10.7.1.
- [231]
T.M. Liggett(1976)
Coupling the simple exclusion process.
Ann. Probab. 4, pp. 339–356.
Cited by: 12.2.
- [232]
T.M. Liggett(1985)
Interacting particle systems.
Springer–Verlag.
Cited by: 1.2.3,
14.4,
14.8,
14.
- [233]
T. Lindstrøm(1989)
Brownian motion on nested fractals.
Memoirs of the A.M.S. 420.
Cited by: 13.4.
- [234]
T. Lindvaal(1992)
Lectures on the coupling method.
Wiley, New York.
Cited by: 12.2,
13.4,
14.7.1,
14.8,
14.8,
14.8,
9.1,
9.7.
- [235]
J.S. Liu, F. Liang and W.H. Wong(xxx)
The use of multiple-try method and local optimization in Metropolis sampling.
JASA xxx, pp. xxx.
Cited by: 11.3.2,
11.3.4,
11.7.
- [236]
J.S. Liu(1996)
Metropolized independent sampling with comparisons to rejection sampling and importance sampling.
Statistics and Computing 6, pp. 113–119.
Cited by: 11.4.2.
- [237]
J.S. Liu(2001)
Monte carlo techniques in scientific computing.
Springer–Verlag.
Cited by: 11.2.2,
11.7,
11.7,
11.
- [238]
L. Lovász and M. Simonovits(1990)
The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume.
pp. 346–355.
Cited by: 10.6,
4.7.
- [239]
L. Lovász and M. Simonovits(1993)
Random walks in a convex body and an improved volume algorithm.
Random Struct. Alg. 4, pp. 359–412.
Cited by: 10.6.
- [240]
L. Lovász and P. Winkler(1995)
Efficient stopping rules for Markov chains.
pp. 76–82.
Cited by: 2.10.1,
2.9,
4.7,
9.3.1,
9.6.1,
9.7.
- [241]
L. Lovász and P. Winkler(1995)
Exact mixing in an unknown Markov chain.
Electronic J. Combinatorics 2, pp. #R15.
Cited by: 9.3.1,
9.7.
- [242]
L. Lovász(1993)
Combinatorial problems and exercises.
North-Holland.
Note: Second Edition
Cited by: 1.2.3.
- [243]
A. Lubotzky(1994)
Discrete groups, expanding graphs and invariant measures.
Birkhauser.
Note: Progress in Mathematics, vol. 125
Cited by: 10.1.1,
10.1.1,
13.3.1,
13.4.
- [244]
M. Luby and E. Vigoda(1999)
Fast convergence of the Glauber dynamics for sampling independent sets.
Technical report
ICSI, Berkeley CA.
Cited by: 12.1.12,
12.2.
- [245]
R. Lyons, R. Pemantle and Y. Peres(1995)
Ergodic theory on Galton–Watson trees: speed of random walk and dimension of harmonic measure.
Ergodic Theory Dynam. Systems 15, pp. 593–619.
Cited by: 13.3.3,
13.3.3.
- [246]
R. Lyons, R. Pemantle and Y. Peres(1996)
Biased random walks on Galton–Watson trees.
Probab. Th. Rel. Fields 106, pp. 249–264.
Cited by: 13.3.3,
13.3.3,
13.3.3.
- [247]
R. Lyons, R. Pemantle and Y. Peres(1996)
Unsolved problems concerning random walks on trees.
in K. Athreya and P. Jagers (Eds.), Classical and Modern Branching Processes,
pp. 223–238.
Cited by: 13.3.3,
13.4.
- [248]
R. Lyons and R. Pemantle(1992)
Random walk in a random environment and first-passage percolation on trees.
Ann. Probab. 20, pp. 125–136.
Cited by: 13.3.3.
- [249]
R. Lyons and Y. Peres(2002)
Probability on trees and networks.
Cambridge University Press.
Note: In preparation
Cited by: 13.3.3,
13.4,
3.8,
9.7.
- [250]
R. Lyons(1992)
Random walks, capacity, and percolation on trees.
Ann. Probab. 20, pp. 2043–2088.
Cited by: 5.4.
- [251]
T.J. Lyons(1983)
A simple criterion for transience of a reversible Markov chain.
Ann. Probab. 11, pp. 393–402.
Cited by: 3.8.
- [252]
N. Madras and G. Slade(1993)
The self-avoiding walk.
Birkhauser.
Cited by: 11.1.2.
- [253]
M. B. Marcus and J. Rosen(1992)
Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes.
Ann. Probab. 20, pp. 1603–1684.
Cited by: 14.6.2.
- [254]
E. Marinari and G. Parisi(1992)
Simulated tempering: a new Monte Carlo scheme.
Europhysics Letters 19, pp. 451–458.
Cited by: 11.3.3.
- [255]
P.C. Matthews(1985)
Covering problems for random walks on spheres and finite groups.
Ph.D. Thesis, Statistics, Stanford.
Cited by: 7.4.
- [256]
P.C. Matthews(1988)
A strong uniform time for random transpositions.
J. Theoretical Probab. 1, pp. 411–423.
Cited by: 4.7.
- [257]
P.C. Matthews(1988)
Covering problems for Brownian motion on spheres.
Ann. Probab. 16, pp. 189–199.
Cited by: 2.9,
2.26.
- [258]
P.C. Matthews(1988)
Covering problems for Markov chains.
Ann. Probab. 16, pp. 1215–1228.
Cited by: 2.9,
7.1.5,
7.4.
- [259]
P.C. Matthews(1990)
Mixing rates for Brownian motion in a convex polyhedron.
J. Appl. Probab. 27, pp. 259–268.
Cited by: 13.4.
- [260]
P.C. Matthews(1992)
Strong stationary times and eigenvalues.
J. Appl. Probab. 29, pp. 228–233.
Cited by: 4.7.
- [261]
J.E. Mazo(1982)
Some extremal Markov chains.
Bell System Tech. J. 61, pp. 2065–2080.
Cited by: 5.4.
- [262]
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller(1953)
Equations of state calculations by fast computing machine.
J. Chem. Phys. 21, pp. 1087–1091.
Cited by: 11.7.
- [263]
S.P. Meyn and R.L. Tweedie(1993)
Markov chains and stochastic stability.
Springer–Verlag.
Cited by: 13.4,
13.4,
2.9,
4.7.
- [264]
J.W. Moon(1973)
Random walks on random trees.
J. Austral. Math. Soc. 15, pp. 42–53.
Cited by: 13.3.4,
13.3.4,
13.4,
5.4.
- [265]
R. Motwani and P. Raghavan(1995)
Randomized algorithms.
Cambridge University Press.
Cited by: 1.2.2,
10.3.1,
10.6,
10.6,
10.6,
10.6.
- [266]
C. St. J. A. Nash-Williams(1959)
Random walks and electric currents in networks.
Proc. Cambridge Philos. Soc. 55, pp. 181–194.
Cited by: 3.8.
- [267]
R.M. Neal(1996)
Bayesian learning for neural networks.
Lecture Notes in Statistics, Springer–Verlag.
Cited by: 11.7.
- [268]
R.M. Neal(1996)
Sampling from multimodal distributions using tempered transitions.
Statistics and Computing 6, pp. 353–366.
Cited by: 11.7.
- [269]
C. Neuhauser and A. Sudbury(1993)
The biased annihilating branching process.
Adv. in Appl. Probab. 25, pp. 24–38.
Cited by: 14.6.1.
- [270]
J.R. Norris(1997)
Markov chains.
Cambridge University Press.
Cited by: 1.2.3,
12.2,
13.1.1,
2.1.1,
2.1.2,
2.1,
2.1,
2.9,
2.1,
2.2.
- [271]
I. Pak(1999)
Random walk on finite groups with few random generators.
Electon. J. Probab. 4 (1), pp. 1–11.
Cited by: 13.4.
- [272]
J. L. Palacios(1990)
Bounds on expected hitting times for a random walk on a connected graph.
Linear Algebra Appl. 141, pp. 241–252.
Cited by: 5.4.
- [273]
J. L. Palacios(1992)
A bound for the covering time of random walks on graphs.
Statistics and Probab. Lett. 14, pp. 9–11.
Cited by: 6.9.
- [274]
J. L. Palacios(1992)
Expected cover times of random walks on symmetric graphs.
J. Theoretical Probab. 5, pp. 597–600.
Cited by: 7.4.
- [275]
J. L. Palacios(1993)
Fluctuation theory for the Ehrenfest urn model via electrical networks.
Adv. in Appl. Probab. 25, pp. 472–476.
Cited by: 5.4,
7.3.2.
- [276]
J.L. Palacios(1990)
On a result of Aleliunas et al. concerning random walks on graphs.
Prob. Engineering Inform. Sci. 4, pp. 489–492.
Cited by: 6.9.
- [277]
L. Pearce(1980)
Random walks on trees.
Discrete Math. 30, pp. 269–276.
Cited by: 5.3.2.
- [278]
R. Pemantle(1991)
Choosing a spanning tree for the integer lattice uniformly.
Ann. Probab. 19, pp. 1559–1574.
Cited by: 9.7.
- [279]
R. Pemantle(1995)
Uniform random spanning trees.
Boca Raton, FL, pp. 1–54.
Cited by: 9.2.2,
9.7,
9.7.
- [280]
P. Peskun(1973)
Optimal Monte Carlo sampling using Markov chains.
Biometrika 60, pp. 607–612.
Cited by: 11.1,
11.5,
3.4.
- [281]
N. Pippenger(1977)
Superconcentrators.
SIAM J. Comput. 6, pp. 298–304.
Cited by: 13.4.
- [282]
J.W. Pitman(1976)
On coupling of Markov chains.
Z. Wahrsch. Verw. Gebiete 35, pp. 313–322.
Cited by: 12.2.
- [283]
J.W. Pitman(1977)
Occupation measures for Markov chains.
Adv. in Appl. Probab. 9, pp. 69–86.
Cited by: 2.9.
- [284]
U. Porod(1995)
lower bounds for a special class of random walks.
Probab. Th. Rel. Fields 101, pp. 277–289.
Cited by: 13.4.
- [285]
U. Porod(1996)
The cut-off phenomenon for random reflections.
Ann. Probab. 24, pp. 74–96.
Cited by: 13.1.5,
13.4.
- [286]
J. Propp and D. Wilson(1996)
Exact sampling with coupled Markov chains and applications to statistical mechanics.
Random Struct. Alg. 9, pp. 223–252.
Cited by: 9.3.3.
- [287]
Y. Rabani, Y. Rabinovich and A. Sinclair(1995)
A computational view of population genetics.
pp. 83–92.
Cited by: 12.2.
- [288]
P. Revesz(1990)
Random walk in random and non-random scenery.
World Scientific, Singapore.
Cited by: 7.4.
- [289]
D. Revuz(1984)
Markov chains.
Second edition, North-Holland.
Cited by: 2.9,
9.7.
- [290]
C.P. Robert and G. Casella(2000)
Monte carlo statistical methods.
Springer–Verlag.
Cited by: 11.7.
- [291]
C.P. Robert (Ed.)(1998)
Discretization and MCMC convergence assesment.
Lecture Notes in Statistics, Springer–Verlag.
Cited by: 11.7.
- [292]
G.O. Roberts, A. Gelman and W.R. Gilks(1997)
Weak convergence and optimal scaling of random walk Metropolis algorithms.
Ann. Appl. Probab. 7, pp. 110–120.
Cited by: 11.5.1,
11.5.2.
- [293]
G.O. Roberts and R.L. Tweedie(1996)
Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms.
Biometrika 83, pp. 95–110.
Cited by: 11.7.
- [294]
G.O. Roberts(1998)
Optimal Metropolis algorithms for product measures on the vertices of a hypercube.
Stochastics Stochastic Rep. 62, pp. 275–283.
Cited by: 11.5.2.
- [295]
L.C.G. Rogers and D. Williams(1994)
Diffusions, Markov processes and martingales: foundations.
Second edition, Vol. 1, Wiley.
Cited by: 13.4.
- [296]
Y. Roichman(1996)
On random random walks.
Ann. Probab. 24, pp. 1001–1011.
Cited by: 13.3.1.
- [297]
V. I. Romanovsky(1970)
Discrete markov chains.
Wolthers-Noordhoff.
Note: English translation of Russian original
Cited by: 2.9.
- [298]
J. S. Rosenthal(1994)
Random rotations: characters and random walks on .
Ann. Probab. 22, pp. 398–423.
Cited by: 13.4.
- [299]
S. M. Ross(1981)
A random graph.
J. Appl. Probab. 18, pp. 309–315.
Cited by: 9.3.1.
- [300]
S. Ross(1983)
Stochastic processes.
Wiley.
Cited by: 2.2.1.
- [301]
H. Rost(1971)
The stopping distributions of a Markov process.
Inventiones Math. 14, pp. 1–16.
Cited by: 2.10.1,
9.7.
- [302]
O. S. Rothaus(1981)
Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities.
J. Funct. Anal. 42, pp. 102–109.
Cited by: 8.4.1.
- [303]
W. Rudin(1987)
Real and complex analysis.
3rd edition, McGraw–Hill Book Co., New York.
Cited by: 8.2.2.
- [304]
L. Saloff-Coste(1997)
Lectures on finite Markov chains.
Lectures on probability theory and statistics (Saint-Flour,
1996),
pp. 301–413.
Cited by: 8.6.
- [305]
P. Sarnak(1990)
Some applications of modular forms.
Cambridge University Press.
Note: Cambridge Tracts in Math. 99
Cited by: 13.4.
- [306]
A.M. Sbihi(1990)
Covering times for random walks on graphs.
Ph.D. Thesis, McGill University.
Cited by: 6.9,
6.9,
6.9,
7.4,
7.4.
- [307]
A. J. Sinclair(1992)
Improved bounds for mixing rates of Markov chains and multicommodity flow.
Combin. Probab. Comput. 1, pp. 351–370.
Cited by: 4.3.5,
4.4.3,
4.7.
- [308]
A. J. Sinclair(1993)
Algorithms for random generation and counting.
Birkhauser.
Cited by: 10.6,
10.6,
10.6.
- [309]
A. Sinclair and M. Jerrum(1989)
Approximate counting, uniform generation and rapidly mixing Markov chains.
Information and Computation 82, pp. 93–133.
Cited by: 4.7.
- [310]
R.L. Smith(1984)
Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions.
Operations Research 32, pp. 1296–1308.
Cited by: 11.7.
- [311]
A.D. Sokal(1989)
Monte Carlo methods in statistical mechanics: foundations and new algorithms.
Cited by: 11.1.2,
11.7.
- [312]
R. Solovay and V. Strassen(1977)
A fast Monte-Carlo test for primality.
SIAM J. Comput. 6, pp. 84–85.
Cited by: 10.8.
- [313]
R. Stanley(1999)
Enumerative combinatorics, vol. 2.
Cambridge University Press.
Cited by: 13.3.4.
- [314]
W.J. Stewart(1995)
Introduction to the numerical solution of Markov chains.
Princeton University Press.
Cited by: 2.9.
- [315]
D. Stoyan(1983)
Comparison methods for queues and other stochastic models.
Wiley.
Cited by: 14.8.
- [316]
W.G. Sullivan(1984)
spectral gap and jump processes.
Z. Wahrsch. Verw. Gebiete 67, pp. 387–398.
Cited by: 9.7.
- [317]
D.E. Symer(1984)
Expanded ergodic Markov chains and cycling systems.
Note: Senior thesis, Dartmouth College
Cited by: 9.7.
- [318]
R. Syski(1992)
Passage times for Markov chains.
IOS Press, Amsterdam.
Cited by: 2.9.
- [319]
L. Takács(1981)
Random flights on regular polytopes.
SIAM J. Alg. Discrete Meth. 2, pp. 153–171.
Cited by: 7.3.2,
7.4.
- [320]
L. Takács(1984)
Random flights on regular graphs.
Adv. in Appl. Probab. 16, pp. 618–637.
Cited by: 7.3.2,
7.4.
- [321]
M. Tanushev and R. Arratia(1997)
A note on distributional equality in the cyclic tour property for Markov chains.
Combin. Probab. Comput. 6, pp. 493–496.
Cited by: 3.8.
- [322]
A. Telcs(1990)
Spectra of graphs and fractal dimensions I.
Probab. Th. Rel. Fields 85, pp. 489–497.
Cited by: 13.4.
- [323]
A. Telcs(1995)
Spectra of graphs and fractal dimensions II.
J. Theoretical Probab. 8, pp. 77–96.
Cited by: 13.4.
- [324]
P. Tetali and P. Winkler(1993)
Simultaneous reversible Markov chains.
Vol. 1, pp. 433–451.
Cited by: 3.8.
- [325]
P. Tetali(1991)
Random walks and the effective resistance of networks.
J. Theoretical Probab. 4, pp. 101–109.
Cited by: 3.8.
- [326]
P. Tetali(1994)
An extension of Foster’s network theorem.
Combin. Probab. Comput. 3, pp. 421–427.
Cited by: 3.8.
- [327]
P. Tetali(1994)
Design of on-line algorithms using hitting times.
Note: Bell Labs
Cited by: 10.6,
9.4.2.
- [328]
H. Thorisson(2000)
Coupling, stationarity and regeneration.
Springer–Verlag.
Cited by: 13.4.
- [329]
E. van Doorn(1981)
Stochastic monotonicity and queueing applications of birth-death processes.
Lecture Notes in Stat., Vol. 4, Springer–Verlag.
Cited by: 14.8.
- [330]
A.R.D. van Slijpe(1984)
Random walks on regular polyhedra and other distance-regular graphs.
Statist. Neerlandica 38, pp. 273–292.
Cited by: 7.1.3,
7.3.2,
7.4.
- [331]
A.R.D. van Slijpe(1986)
Random walks on the triangular prism and other vertex-transitive graphs.
J. Comput. Appl. Math. 15, pp. 383–394.
Cited by: 7.3.2,
7.4.
- [332]
N. Th. Varopoulos, L. Saloff-Coste and T. Coulhon(1992)
Analysis and geometry on groups.
Cambridge University Press.
Cited by: 1.2.3.
- [333]
E. Vigoda(1999)
Improved bounds for sampling colorings.
Note: C.S. Dept., U.C. Berkeley
Cited by: 12.1.12,
12.2.
- [334]
I.C. Walters(1996)
The ever expanding expander coefficients.
Bull. Inst. Combin. Appl. 17, pp. 79–86.
Cited by: 10.6.
- [335]
K. Weber(1990)
Random spread of information, random graph processes and random walks.
pp. 361–366.
Cited by: 14.8.
- [336]
H.S. Wilf(1989)
The editor’s corner: the white screen problem.
Amer. Math. Monthly 96, pp. 704–707.
Cited by: 1.1.2.
- [337]
H.S. Wilf(1990)
Computer-generated proofs of binomial coefficient idenitites.
Note: U. Penn.
Cited by: 5.4.
- [338]
D.B. Wilson(2004)
Mixing times of lozenge tiling and card shuffling Markov chains.
Ann. Appl. Probab. 14, pp. 274–325.
Cited by: 12.1.9.
- [339]
W. Woess(2000)
Random walks on infinite graphs and groups.
Cambridge Tracts Math., Cambridge Univ. Press.
Cited by: 13.2.10,
13.2.3,
13.2.7,
13.2,
13.4,
13.4.
- [340]
O. Yaron(1988)
Random walks on trees.
Technical report
Hebrew University, Jerusalem.
Cited by: 5.3.2.
- [341]
D. Zuckerman(1989)
Covering times of random walks on bounded degree trees and other graphs.
J. Theoretical Probab. 2, pp. 147–157.
Cited by: 3.8,
6.9.
- [342]
D. Zuckerman(1991)
On the time to traverse all edges in a graph.
Information Proc. Letters. 38, pp. 335–337.
Cited by: 6.1.
- [343]
D. Zuckerman(1992)
A technique for lower bounding the cover time.
SIAM J. Discrete Math. 5, pp. 81–87.
Cited by: 6.9,
6.9,
7.4,
7.4.