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Contents

1978

1. D. Aldous, “Stopping Times and Tightness,” Ann. Probab. 6 (1978) 335-340, MathSciNet.

1981

1. D. Aldous, “Representations for Partially Exchangeable Arrays of Random Variables,” J. Multivariate Anal. 11 (1981) 581-598, MathSciNet.
2. D. Aldous, “Subspaces of L¹, via Random Measures,” Trans. Amer. Math. Soc. 267 (1981) 445-463, MathSciNet.

1981,

1. D. Aldous and M. Barlow, “On Countable Dense Random Sets,” in Seminaire de Probabilites XV, pp. 311-327. Springer-Verlag, 1981. MathSciNet.

1982

1. D. Aldous, “Some Inequalities for Reversible Markov Chains,” J. London Math. Soc. (2) 25 (1982) 564-576, MathSciNet.
2. D. Aldous, “Markov Chains with Almost Exponential Hitting Times,” Stochastic Process. Appl. 13 (1982) 305-310, MathSciNet.

1983

1. D. Aldous and J. Pitman, “The Asymptotic Speed and Shape of a Particle System,” in Probability Statistics and Analysis, J. Kingman and G. Reuter, eds., pp. 1-23. Cambridge University Press, 1983. MathSciNet. London Math. Soc. Lecture Notes 79.
2. D. Aldous, “On the Time Taken by Random Walks on Finite Groups to Visit Every State,” Z. Wahrsch. Verw. Gebiete 62 (1983) 361-374, MathSciNet.
3. D. Aldous, “Random Walks on Finite Groups and Rapidly Mixing Markov Chains,” in Seminaire de Probabilites XVII, pp. 243-297. Springer-Verlag, 1983. MathSciNet. Lecture Notes in Math. 986.
4. D. Aldous, “Minimization Algorithms and Random Walk on the d-cube,” Ann. Probab. 11 (1983) 403-413, MathSciNet.

1985

1. D. Aldous, “Exchangeability and Related Topics,” in École d’Été St Flour 1983, pp. 1-198. Springer-Verlag, 1985. MathSciNet. Lecture Notes in Math. 1117.
2. D. Aldous, “Self-intersections of Random Walks on Discrete Groups,” Math. Proc. Cambridge Philos. Soc. 98 (1985) 155-177, MathSciNet.

1986

1. D. Aldous and P. Diaconis, “Shuffling Cards and Stopping Times,” Amer. Math. Monthly 93 (1986) 333-348, MathSciNet.
2. D. Aldous, “Some Interesting Processes Arising as Heavy Traffic Limits in a M/M/ Storage Process,” Stochastic Proc. Appl. 22 (1986) 291-313, MathSciNet.

1987

1. D. Aldous, “Ultimate Instability of Exponential Backoff Protocol for Acknowledgement-based transmission Control of Random Access Communication Channels,” IEEE Trans. Inf. Th. 33 (1987) 219-223, MathSciNet.
2. D. Aldous and P. Diaconis, “Strong Uniform Times and Finite Random Walks,” Adv. in Appl. Math. 8 (1987) 69-97, MathSciNet.
3. D. Aldous and L. Shepp, “The Least Variable Phase Type Distribution is Erlang,” Stochastic Models 3 (1987) 467-473, MathSciNet.
4. D. Aldous, “On the Markov Chain Simulation Method for Uniform Combinatorial Distributions and Simulated Annealing,” Probab. Engineering Inform. Sci. 1 (1987) 33-46, MathSciNet.

1988

1. D. Aldous, “Hashing with Linear Probing, Under Non-uniform Probabilities,” Probab. Engineering Inform. Sci. 2 (1988) 1-14, MathSciNet.
2. D. Aldous, “Finite-Time Implications of Relaxation Times for Stochastically Monotone Processes,” Probab. Th. Rel. Fields 77 (1988) 137-145, MathSciNet.
3. D. Aldous, B. Flannery, and J. Palacios, “Two Applications of Urn Processes,” Probab. Engineering Inform. Sci. 2 (1988) 293-307, MathSciNet.
4. D. Aldous and P. Shields, “A Diffusion Limit for a Class of Randomly-growing Binary Trees,” Probab. Th. Rel. Fields 79 (1988) 509-542, MathSciNet.

1989

1. D. Aldous, “Stein’s Method in a Two-Dimensional Coverage Problem,” Stat. Probab. Letters 8 (1989) 307-314, MathSciNet.
2. D. Aldous, Probability Approximations via the Poisson Clumping Heuristic. Springer-Verlag, 1989.
3. D. Aldous, “Hitting Times for Random Walks on Vertex-transitive Graphs,” Math. Proc. Cambridge Philos. Soc. 106 (1989) 179-191, MathSciNet.
4. D. Aldous, “Stopping Times and Tightness II,” Ann. Probab. 17 (1989) 586-595, MathSciNet.
5. D. Aldous, “An Introduction to Covering Problems for Random Walks on Graphs,” J. Theoretical Probab. 2 (1989) 87-89, MathSciNet.
6. D. Aldous, “Lower Bounds for Covering Times for Reversible Markov Chains and Random Walks on Graphs,” J. Theoretical Probab. 2 (1989) 91-100, MathSciNet.
7. D. Aldous, “The Harmonic Mean Formula for Probabilities of Unions: Applications to Sparse Random Graphs,” Discrete Math. 76 (1989) 167-176, MathSciNet.

1990

1. D. Aldous, “The Random Walk Construction of Uniform Spanning Trees and Uniform Labelled Trees,” SIAM J. Discrete Math. 3 (1990) 450-465, MathSciNet.
2. D. Aldous and W. Krebs, “The Birth-and-Assassination Process,” Stat. Probab. Letters 10 (1990) 427-430, MathSciNet.
3. D. Aldous, “A Random Tree Model Associated with Random Graphs,” Random Structures Algorithms 1 (1990) 383-402, MathSciNet.
4. D. Aldous and U. Vazirani, “A Markovian Extension of Valiant’s Learning Model,” in Proc. 31st Symp. Foundations of Computer Sci., pp. 392-396. 1990. Extended abstract. Final version to appear in Information and Computation, MathSciNet.

1991

1. D. Aldous, “The Continuum Random Tree I,” Ann. Probab. 19 (1991) 1-28, MathSciNet.
2. D. Aldous, “Threshold Limits for Cover Times,” J. Theoretical Probab. 4 (1991) 197-211, MathSciNet.
3. D. Aldous, B. Fristedt, P. Griffin, and W. Pruitt, “The Number of Extreme Points in the Convex Hull of a Random Sample,” J. Appl. Probab. 28 (1991) 287-304, MathSciNet.
4. D. Aldous, “Applications of Random Walks on Finite Graphs,” in Selected Proceedings of the Sheffield Symposium on Applied Probability, I. Basawa and R. Taylor, eds., pp. 12-26. Institute of Mathematical Statistics, Hayward CA, 1991. Lecture Notes 18, MathSciNet.
5. D. Aldous, “The Continuum Random Tree II: an Overview,” in Stochastic Analysis, M. Barlow and N. Bingham, eds., pp. 23-70. Cambridge University Press, 1991. MathSciNet.
6. D. Aldous, “Random Walk Covering of some Special Trees,” J. Math. Analysis Appl. 157 (1991) 271-283, MathSciNet.
7. D. Aldous, “Meeting Times for Independent Markov Chains,” Stochastic Process. Appl. 38 (1991) 185-193, MathSciNet.
8. D. Aldous, “Asymptotic Fringe Distributions for General Families of Random Trees,” Ann. Appl. Probab. 1 (1991) 228-266, MathSciNet.

1992

1. D. Aldous, “Greedy Search on the Binary Tree with Random Edge-Weights,” Combinatorics, Probability and Computing 1 (1992) 281-293, MathSciNet.
2. D. Aldous and M. Brown, “Inequalities for Rare Events in Time-Reversible Markov Chains I,” in Stochastic Inequalities, M. Shaked and Y. Tong, eds., vol. 22 of Lecture Notes, pp. 1-16. Institute of Mathematical Statistics, 1992. MathSciNet.
3. D. Aldous and J. Steele, “Asymptotics for Euclidean Minimal Spanning Trees on Random Points,” Probab. Th. Rel. Fields 92 (1992) 247-258, MathSciNet.
4. D. Aldous, M. Hofri, and W. Szpankowski, “Maximum Size of a Dynamic Data Structure: Hashing with Lazy Deletion Revisited,” SIAM J. Computing 21 (1992) 713-732, MathSciNet.
5. D. Aldous, “Asymptotics in the Random Assignment Problem,” Probab. Th. Rel. Fields 93 (1992) 507-534, MathSciNet.
6. D. Aldous and B. Larget, “A Tree-based Scaling Exponent for Random Cluster Models,” J. Phys. A: Math. Gen. 25 (1992) L1065-L1069, MathSciNet.
7. D. Aldous and J. Pitman, “Distributional Aspects of a Recursive Decomposition of Brownian Bridge and Random Mapping Asymptotics.” In Preparation, 1992.

1993

1. D. Aldous, “Approximate Counting via Markov Chains,” Statistical Science 8 (1993) 16-19, MathSciNet.
2. D. Aldous and M. Brown, “Inequalities for Rare Events in Time-Reversible Markov Chains II,” Stochastic Process. Appl. 44 (1993) 15-25, MathSciNet.
3. D. Aldous and H. Thorisson, “Shift-Coupling,” Stochastic Process. Appl. 44 (1993) 1-14, MathSciNet.
4. D. Aldous, “The Continuum Random Tree III,” Ann. Probab. 21 (1993) 248-289, MathSciNet.
5. D. Aldous, “A Note on Probabilistic Analysis of a Sparse Matrix Factorization Scheme and Random Graphs,” Probab. Engineering Inform. Sci. 7 (1993) 465-469, MathSciNet.
6. D. Aldous, “Tree-Based Models for Random Distribution of Mass,” J. Statist. Phys. 73 (1993) 625-641, MathSciNet.

1994

1. D. Aldous, “Recursive Self-Similarity for Random Trees, Random Triangulations and Brownian Excursion,” Ann. Probab. 22 (1994) 527-545, MathSciNet.
2. D. Aldous and J. Pitman, “Brownian Bridge Asymptotics for Random Mappings,” Random Structures Algorithms 5 (1994) 487-512, MathSciNet.
3. D. Aldous, “Triangulating the Circle, at Random,” Amer. Math. Monthly 101 (1994) 223-233, MathSciNet.
4. D. Aldous and U. Vazirani, “Go With the Winners Algorithms,” in Proc. 35th Symp. Foundations of Computer Sci., pp. 492-501. IEEE Computer Soc. Press, 1994. MathSciNet.

1995

1. D. Aldous, “A Family of Self-Similar Continuous Interval-Splitting Processes.” In Preparation, 1995.
2. D. Aldous, “Probability Distributions on Cladograms,” in Random Discrete Structures, D. Aldous and R. Pemantle, eds., vol. 76 of IMA Volumes in Mathematics and its Applications, pp. 1-18. Springer-Verlag, 1995. MathSciNet.
3. D. Aldous and U. Vazirani, “A Markovian Extension of Valiant’s Learning Model,” Information and Computation 117 (1995) 181-186, MathSciNet.
4. D. Aldous, “On Simulating a Markov Chain Stationary Distribution When Transition Probabilities are Unknown,” in Discrete Probability and Algorithms, D. Aldous, P. Diaconis, J. Spencer, and J. M. Steele, eds., vol. 72 of IMA Volumes in Mathematics and its Applications, pp. 1-9. Springer-Verlag, 1995. MathSciNet.
5. D. Aldous, “Probability Distributions on Cladograms,” in Random Discrete Structures, D. Aldous and R. Pemantle, eds., vol. 76 of IMA Volumes in Mathematics and its Applications, pp. 1-18. Springer-Verlag, 1995. Available via homepage http://www.stat.berkeley.edu/~aldous, MathSciNet.
6. D. Aldous and P. Diaconis, “Hammersley’s Interacting Particle Process and Longest Increasing Subsequences,” Probab. Th. Rel. Fields 103 (1995) 199-213, MathSciNet.
7. D. Aldous, “Darwin’s Log: A Toy Model of Speciation and Extinction,” J. Appl. Probab. 32 (1995) 279-295, MathSciNet.
8. D. Aldous, “How Should We Classify Combinatorial Optimization Problems Under Probability Models?.” In Preparation, 1995.

1997

1. D. Aldous and J. Pitman, “Tree- and Forest-Valued Markov Chains.” In Preparation, 1997.
2. D. Aldous, L. Lovász, and P. Winkler, “Mixing Times for Uniformly Ergodic Markov Chains,” Stochastic Process. Appl. 71 (1997) 165-185, MathSciNet.
3. D. Aldous, “Brownian Excursions, Critical Random Graphs and the Multiplicative Coalescent,” Ann. Probab. 25 (1997) 812-854, MathSciNet.

1998

1. D. Aldous, “On the Critical Value for Percolation of Minimum-Weight Trees in the Mean-Field Distance Model,” Combin. Probab. Comput. 7 (1998) 1-10, MathSciNet.
2. D. Aldous, “Brownian Excursion Conditioned on its Local Time,” Elect. Comm. in Probab. 3 (1998) 79-90, MathSciNet.
3. D. Aldous and J. Pitman, “The Standard Additive Coalescent,” Ann. Probab. 26 (1998) 1703-1726, MathSciNet.
4. D. Aldous, “Stochastic Coalescence,” in Proc. I.C.M. 1998, volume 3. Special vol. of Documenta Mathematica, G. Fischer and U. Rehmann, eds., pp. 205-211. 1998. MathSciNet.
5. D. Aldous, “A Metropolis-Type Optimization Algorithm on the Infinite Tree,” Algorithmica 22 (1998) 388-412, MathSciNet.
6. D. Aldous, “Tree-Valued Markov Chains and Poisson-Galton-Watson Distributions,” in Microsurveys in Discrete Probability, D. Aldous and J. Propp, eds., no. 41 in DIMACS Ser. Discrete Math. Theoret. Comp. Sci, pp. 1-20. Amer. Math. Soc., 1998. MathSciNet.
7. D. Aldous, “Emergence of the Giant Component in Special Marcus-Lushnikov Processes,” Random Structures Algorithms 12 (1998) 179-196, MathSciNet.
8. D. Aldous and V. Limic, “The Entrance Boundary of the Multiplicative Coalescent,” Electron. J. Probab. 3 (1998) 1-59, MathSciNet.
9. D. Aldous and J. Pitman, “Tree-valued Markov Chains Derived from Galton-Watson Processes,” Ann. Inst. H. Poincarè Probab. Statist. 34 (1998) 637-686, MathSciNet.

1999

1. D. Aldous and J. Pitman, “A Family of Random Trees with Random Edge Lengths,” Random Structures Algorithms 15 (1999) 176-195, MathSciNet.
2. D. Aldous and P. Diaconis, “Longest Increasing Subsequences: From Patience Sorting to the Baik-Deift-Johansson Theorem,” Bull. Amer. Math. Soc. 36 (1999) 413-432, MathSciNet.
3. D. Aldous and S. N. Evans, “Dirichlet Forms on Totally Disconnected Spaces and Bipartite Markov Chains,” J. Theoretical Probab. 12 (1999) 839-857, MathSciNet.
4. D. Aldous, “The Moran Process as a Markov Chain on Leaf-labeled Trees.” Unpublished, 1999.
5. D. Aldous, “Deterministic and Stochastic Models for Coalescence (Aggregation and Coagulation): a Review of the Mean-Field Theory for Probabilists,” Bernoulli 5 (1999) 3-48, MathSciNet.

2000

1. D. Aldous, “The Percolation Process on a Tree where Infinite Clusters are Frozen,” Math. Proc. Cambridge Philos. Soc. 128 (2000) 465-477, MathSciNet.
2. D. Aldous and J. Pitman, “Inhomogeneous Continuum Random Trees and the Entrance Boundary of the Additive Coalescent,” Probab. Th. Rel. Fields 118 (2000) 455-482, MathSciNet.
3. D. Aldous and B. Pittel, “On a Random Graph with Immigrating Vertices: Emergence of the Giant Component,” Random Structures Algorithms 17 (2000) 79-102, MathSciNet.
4. D. Aldous, “Mixing Time for a Markov Chain on Cladograms,” Combin. Probab. Comput. 9 (2000) 191-204, MathSciNet.

2001

1. D. Aldous and J. Fill, “Reversible Markov Chains and Random Walks on Graphs.” Book in preparation, 2001.
2. D. Aldous, “Stochastic Models and Descriptive Statistics for Phylogenetic Trees, from Yule to Today,” Statist. Sci. 16 (2001) 23-34, MathSciNet.
3. D. Aldous, “Reorganizing Large Web Sites,” Amer. Math. Monthly 108 (2001) 16-27, MathSciNet.
4. D. Aldous and A. Bandyopadhyay, “How to Combine Fast Heuristic Markov Chain Monte Carlo with Slow Exact Sampling,” Elect. Comm. in Probab. 6 (2001) 79-89, MathSciNet.
5. D. Aldous, “The (2) limit in the random assignment problem,” Random Structures Algorithms 18 (2001) 381-418, MathSciNet.
6. D. Aldous, M. Miyazawa, and T. Rolski, “On the Stability of a Batch Clearing System with Poisson Arrivals and Subadditive Service Times,” J. Appl. Probab. 38 (2001) 621-634, MathSciNet.

2002

1. D. Aldous and J. Steele, “Asymptotic Essential Uniqueness and its Scaling Exponent for Minimal Spanning Trees on Random Points.” In preparation, 2002.
2. D. Aldous, G. Miermont, and J. Pitman, “Brownian Bridge Asymptotics for Random p-Mappings,” Tech. Rep. 624, Dept. Statistics, U.C. Berkeley, 2002.
3. D. Aldous and J. Pitman, “The asymptotic distribution of the diameter of a random mapping,” C. R. Math. Acad. Sci. Paris 334 (2002) 1021-1024, MathSciNet.
4. D. J. Aldous and J. Pitman, “Two recursive decompositions of Brownian bridge related to the asymptotics of random mappings,” Tech. Rep. 595, Dept. Statistics, U.C. Berkeley, 2002.
5. D. Aldous and J. Pitman, “Invariance Principles for Non-uniform Random Mappings and Trees,” in Asymptotic Combinatorics with Applications to Mathematical Physics, V. Malyshev and A. Vershik, eds., pp. 113-147. Kluwer, 2002. MathSciNet.
6. D. Aldous and A. Bandyopadhyay, “A Survey of Max-type Recursive Distributional Equations.” In preparation, 2002.
7. D. Aldous and P. Diaconis, “The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results,” J. Statist. Phys. 107 (2002) 945-975, MathSciNet.

2003

1. D. Aldous, “A non-rigorous scaling law in mean-field first passage percolation.” Unpublished, 2003.
2. D. Aldous, “Notes on STAT 206.” http://www.stat.berkeley.edu/~aldous/Networks/index.html, 2003.
3. D. Aldous and J. Steele, “The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence.” To appear in Discrete and Combinatorial Probability, H. Kesten (ed.), Springer, 2003.
4. D. Aldous and A. G. Percus, “Scaling and Universality in Continuous Length Combinatorial Optimization.” arXiv:cond-mat/0301035, 2003.

1976

1. D. J. Aldous, “Subsequences of sequences of random variables,” Bull. Amer. Math. Soc. 83 (1976), no. 1, 121-123, MathSciNet.
2. D. J. Aldous, “A characterisation of Hilbert space using the central limit theorem,” J. London Math. Soc. (2) 14 (1976), no. 2, 376-380, MathSciNet.

1977

1. D. J. Aldous, “Limit theorems for subsequences of arbitrarily-dependent sequences of random variables,” Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 40 (1977), no. 1, 59-82, MathSciNet.

1978

1. D. J. Aldous, “Weak convergence of randomly indexed sequences of random variables,” Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 117-126, MathSciNet.
2. D. J. Aldous and G. K. Eagleson, “On mixing and stability of limit theorems,” Ann. Probability 6 (1978), no. 2, 325-331, MathSciNet.

1979

1. D. Aldous and J. Pitman, “On the zero-one law for exchangeable events,” Ann. Probab. 7 (1979), no. 4, 704-723, MathSciNet.
2. D. J. Aldous, “Unconditional bases and martingales in L_p(F),” Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 1, 117-123, MathSciNet.

1981/82

1. D. J. Aldous and D. H. Fremlin, “Colacunary sequences in L-spaces,” Studia Math. 71 (1981/82), no. 3, 297-304, MathSciNet.

1981

1. D. J. Aldous, “On -convergence of Markov chains,” Math. Proc. Cambridge Philos. Soc. 90 (1981), no. 2, 331-333, MathSciNet.

1982

1. D. J. Aldous, “On exchangeability and conditional independence,” in Exchangeability in probability and statistics (Rome, 1981), pp. 165-170. North-Holland, Amsterdam, 1982. MathSciNet.
2. D. J. Aldous, “Partial exchangeability and -topologies,” in Exchangeability in probability and statistics (Rome, 1981), pp. 23-38. North-Holland, Amsterdam, 1982. MathSciNet.

1983

1. D. J. Aldous, “Corrigenda: “Markov chains with almost exponential hitting times”,” Stochastic Process. Appl. 14 (1983), no. 1, 107, MathSciNet.
2. D. J. Aldous, “Tail behavior of birth-and-death and stochastically monotone processes,” Z. Wahrsch. Verw. Gebiete 62 (1983), no. 3, 375-394, MathSciNet.

1986

1. D. J. Aldous, “Self-intersections of 1-dimensional random walks,” Probab. Theory Relat. Fields 72 (1986), no. 4, 559-587, MathSciNet.
2. D. J. Aldous, “Classical convergence of triangular arrays, stable laws and Schauder’s fixed-point theorem,” Adv. in Appl. Probab. (1986), no. suppl., 9-14, MathSciNet.

1989

1. D. Aldous, Probability approximations via the Poisson clumping heuristic, vol. 77 of Applied Mathematical Sciences. Springer-Verlag, New York, 1989.

1992

1. D. Aldous, “Approximate counting via Markov chains,” in Probability and algorithms, pp. 31-38. Nat. Acad. Press, Washington, DC, 1992. MathSciNet.

1995

1. D. Aldous, P. Diaconis, and J. Spencer, eds., Discrete probability and algorithms, vol. 72 of The IMA Volumes in Mathematics and its Applications. Springer-Verlag, New York, 1995. Papers from the Workshops on Probability and Algorithms and The Finite Markov Chain Renaissance held at the University of Minnesota, Minneapolis, Minnesota, 1993.

1996

1. D. Aldous, “Probability distributions on cladograms,” in Random discrete structures (Minneapolis, MN, 1993), vol. 76 of IMA Vol. Math. Appl., pp. 1-18. Springer, New York, 1996. MathSciNet.
2. D. Aldous and R. Pemantle, eds., Random discrete structures, vol. 76 of The IMA Volumes in Mathematics and its Applications. Springer-Verlag, New York, 1996. Papers from the workshop held in Minneapolis, Minnesota, November 15-19, 1993.

1998

1. D. Aldous and J. Propp, eds., Microsurveys in discrete probability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 41. American Mathematical Society, Providence, RI, 1998. Papers from the workshop held as part of the Dimacs Special Year on Discrete Probability in Princeton, NJ, June 2-6, 1997.