Papers

 

  1. Noise Stability of Weighted Majority (Y. Peres). 
  2. Minimal Spanning Forests. (R. Lyons, Y. Peres, and O. Schramm).  Preprint.
  3. Fluctuation of planar Brownian loop capturing large area. (A. Hammond and Y. Peres). 
  4. Scaling limits of the uniform spanning tree and loop-erased random walk on finite graphs. (Yuval Peres and D. Revelle).  Submitted.
  5. Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces. (A. Naor, Y. Peres, O. Schramm and S. Sheffield).  Preprint.
  6. An LIL for cover times of disks by planar random walk and Wiener sausage. (J. B. Hough and Y. Peres).  Trans. Amer. Math. Soc.  To appear.
  7. Recurrent graphs where two independent random walks collide finitely often. (M. Krishnapur and Y. Peres).  Electron. Comm. Probab. 9 (2004), 72--81.
  8. The sharp Hausdorff measure condition for length of projections. (Y. Peres and B. Solomyak).  Proceedings Amer. Math. Soc.  To appear.
  9. Shuffling by semi-random transpositions. (E. Mossel, Y. Peres and A. Sinclair).  45th Symposium on Foundations of Comp. Sci.  To appear.
  10. What is the probability of intersecting the set of Brownian double points? (R. Pemantle and Y. Peres). 
  11. Mixing times for random walks on finite lamplighter groups. (Y. Peres and D. Revelle).  Electron. Journal Probab.  9 (2004), 825--45.
  12. Bootstrap percolation on infinite trees and non-amenable groups. (J. Balogh, Y. Peres and G. Pete).  Combinatorics, Probability & Computing.  To appear.
  13. Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process. (Y. Peres and B. Virág). Acta Math.  To appear.
  14. Fast Simulation of New Coins From Old. (S. Nacu and Y. Peres).  Annals of Applied Probability.  15, no. 1A (2005).
  15. An invariant of finitary codes with finite expected square root coding length. (N. Harvey and Y. Peres).  Ergodic Theory and Dynamical Systems.  To appear
  16. Glauber Dynamics on Trees and Hyperbolic Graphs. (N. Berger,  C. Kenyon, E. Mossel and Y. Peres) Probability Theory and Related Fields.  To appear.  Prelim. version by C. Kenyon, E. Mossel and Y. Peres appeared in   42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001), 568--578.
  17. Extra heads and invariant allocations. (A. Holroyd and Y. Peres). The Annals of Probability. 33, no.1 (2005).
  18. Evolving sets, mixing and heat kernel bounds. (B. Morris and Y. Peres).  Prob. Theory and Related Fields.  To appear.
  19. On the Maximum Satisfiability of Random Formulas. (D. Achlioptas, A. Naor and Y. Peres).  Preprint.
  20. The Threshold for Random k-SAT is 2^k ln2 - O(k). (D. Achlioptas and Y. Peres).  J. Amer. Math. Soc. 17,  no. 4, (2004), 947--973.
  21. Brownian intersections, cover times and thick points via trees. (Y. Peres). Proceedings of the ICM, Beijing 2002, vol. 3, 73--78
  22. Identifying several biased coins encountered by a hidden random walk. (D. Levin, Y. Peres). Rand. Struct. and Alg. 25, no. 1, (2004), 91--114.
  23. New coins from old: computing with unknown bias. (E. Mossel and Y. Peres).  Combinatorica.  To appear.
  24. Anchored Expansion, Percolation and Speed.  (D. Chen, Y. Peres, G. Pete).  Annals of Probability 32, no. 4, (2004).
  25. Late Points for Random Walks in Two Dimensions. (A. Dembo, Y. Peres, J. Rosen, O. Zeitouni).  Annals of Probability.  To appear.
  26. The speed of biased random walk on percolation clusters. (N. Berger, N. Gantert, and Y. Peres). Probab. Theory Related Fields 126, no. 2, (2003), 221--242.
  27. Transience of percolation clusters on wedges. (O. Angel, I. Benjamini, N. Berger and Y. Peres).  Electron. J. Probab.  To appear.
  28. Cover Times for Brownian Motion and Random Walks in Two Dimensions. (A. Dembo, Y. Peres, J. Rosen, and O. Zeitouni).  Ann. Math., 160 (2004).
  29. Markov Chain Intersections and the Loop-Erased Walk. (R. Lyons, Y. Peres and Oded Schramm) Ann. Inst. H. Poincar\'e Probab. Statist. 39, no. 5, (2003), 779--791.
  30. Markov chain intersections and the loop-erased walk. (R. Lyons, Y. Peres and O. Schramm.) Ann. Inst. H. Poincare Probab. Statist. 39 (2003), no. 5, 779--791.

    Let $X$ and $Y$ be independent transient Markov chains on the same state space that have the same transition probabilities. Let $L$ denote the ``loop-erased path'' obtained from the path of $X$ by erasing cycles when they are created. We prove that if the paths of $X$ and $Y$ have infinitely many intersections a.s., then $L$ and $Y$ also have infinitely many intersections a.s.}

  31. Which properties of a random sequence are dynamically sensitive? (I. Benjamini, O. Haggstrom, Y. Peres and J. Steif). Ann. Probab. 31 no. 1  (2003), 1--34.
  32. Geometry of the uniform spanning forest: phase transitions in dimensions 4,8,12,... (I. Benjamini, H. Kesten, Y. Peres and O. Schramm.) Ann. Math. To appear.

    The uniform spanning forest (USF) in $Z^d$ is the weak limit of random, uniformly chosen, spanning trees in the cube $[-n,n]^d$. R. Pemantle (1991) proved that the USF consists a.s. of a single tree if and only if $d<5$. We prove that any two components of the USF in $Z^d$ are adjacent a.s. if $d$ is between 5 and 8 (inclusive), but not if $d>8$. More generally, let $N(x,y)$ be the minimum number of edges outside the USF in a path joining $x$ and $y$ in $Z^d$. Then the maximum of $N(x,y)$, over $x,y$ in $Z^d$, equals almost surely the integer part of (d-1)/4. A new notion of stochastic dimension is introduced and used in the proof.

  33. Information flow on trees (Elchanan Mossel and Y. Peres).  Ann. Appl Prob. 13 no. 3  (2003), 817--844.

    Consider a tree network $T$, where each edge acts as an independent copy of a given channel $M$, and information is propagated from the root. For which $T$ and $M$ does the configuration obtained at level $n$ of $T$ typically contain significant information on the root variable? This problem arose independently in biology, information theory and statistical physics. For all $b$, we construct a channel for which the variable at the root of the $b$-ary tree is independent of the configuration at level $2$ of that tree, yet for sufficiently large $B>b$, the mutual information between the configuration at level $n$ of the $B$-ary tree and the root variable is bounded away from zero. This is related to certain secret-sharing protocols.

  34. Thick Points for Intersections of Planar Sample Paths (A. Dembo, Y. Peres, J. Rosen and O. Zeitouni). Trans. Amer. Math. Soc. 354, no. 12, (2002), 2969--5003.
  35. How likely is Buffon's needle to fall near a planar Cantor set? (Y. Peres and B. Solomyak).  Pacific J. Math. 204, no. 2 (2002), 473--496.
  36. Large Deviations for Random Walks on Galton-Watson Trees: Averaging and Uncertainty. (A. Dembo, N. Gantert, Y. Peres and O. Zeitouni).  Probab. Theory Related Fields 122, no.2, (2002), 241--288.
  37. Bernoulli convolutions and an intermediate value theorem for entropies of K-partitions. (E. Lindenstrauss, Y. Peres and W. Schlag).  J. Anal. Math. 87, (2002), 337--367.
  38. A large Wiener sausage from crumbs (O. Angel, I. Benjamini and Y. Peres) Electronic Comm. Probab. Vol. 5 (2000) Paper no. 7, pages 67-71.
  39. A dimension gap for continued fractions with independent digits (Y. Kifer, Y. Peres and B. Weiss) Israel J. Math. To appear.
  40. Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets (Y. Peres, M. Rams, K. Simon and B. Solomyak).  Proc. Amer. Math. Soc. 129, no. 9, (2001), 2689--2699.
  41. Thin points for Brownian motion. (ps file) (A. Dembo, Y. Peres, J. Rosen and O. Zeitouni). Annales Institut H. Poincare (Probab.) gzipped ps file

    Let T(x,r) denote the occupation measure of the ball of radius r centered at x for Brownian motion {W_t} in dimension d>1, run for unit time. We prove that for any analytic set E in [0,1], the infimum over t in E of the liminf as r tends to 0 of T(W_t,r) |\log r|/(r^2) equals the reciprocal of the packing dimension of E.

  42. Thick points for planar Brownian motion and the Erdos-Taylor conjecture on random walk. (A. Dembo, Y. Peres, J. Rosen and O. Zeitouni).  Acta Math. 186 no. 2, (2001),  239--270.

    Denote by $T(x,r)$ the occupation measure of a disc of radius $r$ around $x$ by planar Brownian motion run till time 1, and let $T(r)$ be the maximum of $T(x,r)$ over $x$ in the plane. We prove that $T(r)$ is a.s. asymptotic to $2 r^2 |\log r|^2$ as $r$ tends to $0$, thus solving a problem posed by Perkins and Taylor (1987). Furthermore, for any $a<2$, the Hausdorff dimension of the set of points $x$ for which $T(x,r)$ is asymptotic to $a r^2 |\log r|^2$, is almost surely $2-a$. As a consequence, we prove a conjecture about planar simple random walk due to Erdos and Taylor (1960): The number of visits to the most frequently visited lattice site in the first $n$ steps of the walk, is asymptotic to $(\log n)^2/\pi$. We also show that for $a$ between 0 and $1/\pi$, the number of points visited more than $a(\log n)^2$ times in the first $n$ steps, is approximately $n^{1-a\pi}$.

  43. Existence of $L^q$ dimensions and entropy dimension for self-conformal measures. (Y. Peres and B. Solomyak).  Indiana Univ. Math. J. 49, no. 4, (2000),  1603--1621.

    We prove the existence of limits in the definitions of $L^q$ dimensions (for all positive $q$ different from 1) as well as the entropy dimension, for any self-conformal measure, without any separation assumptions. We also show the existence of order-two densities for a class of self-similar measures with overlap.

  44. Percolation in a dependent random environment. (Johan Jonasson, Elchanan Mossel and Y. Peres). Random Struct. Alg. 16, (2000), 333--343.

    Draw planes in $\R^3$ that are orthogonal to the $z$ axis, and intersect that axis at the points of a Poisson process with intensity $\lambda$; similarly, draw planes orthogonal to the $x$ and $y$ axes using independent Poisson processes (with the same intensity) on these axes. This yields a randomly stretched rectangular lattice. Consider bond percolation on this lattice where each edge of length $\ell$ is (independently) open with probability $e^{-\ell}$. We show that this model exhibits a phase transition: For large enough $\lambda$, there is an infinite open cluster a.s., and for small $\lambda$, all open clusters are finite a.s. (The question whether the analogous process in two dimensions exhibits a phase transition is open.)

  45. Where did the Brownian particle go? (with R. Pemantle, J. Pitman and M. Yor)  Electron. J. Probab. 6, no. 10,22  (2001) pp. (electronic).
  46. Approximation by polynomials with coefficients 1, -1. (Y. Peres and B. Solomyak.) J. Number Theory , 84, (2000), 185--198.

    In response to a question of R. Kenyon, we prove that the set of polynomials with coefficients $1, -1$, evaluated at a fixed real number $\theta$, is dense in the reals for a.e. $\theta\in (\sqrt{2},2)$. For $\theta \in (1,\sqrt{2}]$, a more complete result can be obtained by elementary methods.

  47. Percolation on nonamenable products at the uniqueness threshold.  (Y. Peres).  Annales Institut H. Poincare (Probab. et Stat.) 36, (2000), 395--406.
  48. Limsup random fractals. (D. Khoshnevisan, Y. Peres and Y. Xiao). Elect. J. Probab. Vol 5, (2000), paper 4, 1-24.
  49. Nonamenable products are not treeable. (R. Pemantle and Y. Peres) Israel Journal of Math 118, (2000), 147--155.
  50. Self-similar sets of zero Hausdorff measure and positive packing measure. (Y. Peres, K. Simon and B. Solomyak).Israel Journal of Math. 117, pp. 353--379 (2000). 
  51. Thick Points for Transient Symmetric Stable Processes. (A. Dembo, Y. Peres, J. Rosen and O. Zeitouni). Elect. J. Probab. 4, (1999), Paper No. 10, 1--13.
  52. Broadcasting on trees and the Ising model. (W. Evans, C. Kenyon, Y. Peres and L. Schulman).  Ann. Appl. Probab. 10, (2000), 410--433. 
  53. Sixty years of Bernoulli convolutions. (Y. Peres, W. Schlag and B. Solomyak). Fractal Geometry and Stochastics II, C. Bandt, S. Graf, and M. Zaehle (editors), Progress in Probability Vol. 46, (2000), Birkhauser, pp. 39--65.
  54. Percolation on Transitive Graphs as a Coalescent Process: Relentless Merging Followed by Simultaneous Uniqueness. (O. Haggstrom, Y. Peres and R. H. Schonmann.) In Perplexing probability problems: Festschrift in Honor of Harry Kesten, (M. Bramson and R. Durrett, Editors), (1999), Birkhauser, pp. 69-90.
  55. Thick points for spatial Brownian motion: multifractal analysis of occupation measure. (A. Dembo, Y. Peres, J. Rosen and O. Zeitouni).To appear, Ann. Probab. 
  56. Crossing estimates and convergence of Dirichlet functions along random walk and diffusion paths. (A. Ancona, R. Lyons and Y. Peres) Ann. Probab. 27 (1999), 970--989.
  57. A phase transition in random coin tossing. (D. Levin R. Pemantle and Y. Peres). Ann. Probab. 29 no. 4, (2001),  1637--1669.
  58. Smoothness of projections, Bernoulli convolutions and the dimension of exceptions. (Y. Peres and W. Schlag.)Duke Math. J. 102, (2000), 193--251. 
  59. Uniform spanning forests. (With I. Benjamini, R. Lyons, Y. Peres and O. Schramm).  Ann. Probab. 29, (2001), 1--65.
  60. Eventual Intersection for Sequences of Levy Processes. (Steven N. Evans and Y. Peres).  Electronic Communications in Probability, Vol. 3 (1998) Paper no. 3, pages 21-27.
  61. Energy and cutsets in infinite percolation clusters. (D. Levin and Y. Peres). Random Walks and Discrete Potential Theory, Cortona 1997, Symposia Mathematica Vol. XXXIX, M. Picardello and W. Woess (editors), Cambridge University Press (1999), 264--278.
  62. Monotonicity of uniqueness for percolation on Cayley graphs: All infinite clusters are born simultaneously. (O. Haggstrom and Y. Peres). Probab. Th. Rel. Fields. 113, (1999), 273--285.
  63. Critical percolation on any nonamenable group has no infinite clusters. (I. Benjamini, R. Lyons, Y. Peres and O. Schramm.) Ann. Probab. 27, (1999), 1347--1356.
  64. Entropy of Convolutions on the Circle. (E. Lindenstrauss, D. Meiri and Y. Peres) Ann. Math. 149, (1999), 871--904.

    For ergodic $p$-invariant measures on the 1-torus $T$, we give a sharp condition on their entropies, implying that the entropy of the convolution converges to $\log p$. We also obtain the following corollary concerning Hausdorff dimension of sum sets: For any sequence ${S_i}$ of $p$-invariant closed subsets of $T$, with Hausdorff dimensions ${d_i}$, if $\sum d_i/|log d_i|$ diverges , then $\dim(S_1 + ... + S_n)$ converges to 1.

  65. Group-invariant percolation on graphs. (I. Benjamini, R. Lyons, Y. Peres and O. Schramm.) Geom. Func. Anal. 9 (1999), 29--66.
  66. Resistance bounds for first passage percolation and maximum flow.  (R. Lyons, R. Pemantle and Y. Peres) J. Combin. Theory Ser. A, 86 (1999), 158--168.
  67. Intersection-equivalence of Brownian paths and certain branching processes (Y. Peres). Comm. Math. Phys. 177 (1996), 417--434. We show that sample paths of Brownian motion (and other stable processes) intersect the same sets as certain random Cantor sets (arising from "fractal percolation" ) which correspond to a branching process. This yields estimates for the intersection probability of several random walk paths in space. (Pictures due to Ofer Licht ). The proof is based on three ingredients:
    1. Classical capacity estimates for Brownian hitting probabilities;
    2. Russell Lyons' capacity estimates for percolation probabilities on trees;
    3. The equivalence between capacities on trees and in Euclidean space.
    (For a unified approach to the first two topics see Martin capacity for Markov chains.)
  68. Unpredictable Paths and Percolation. (I. Benjamini, R. Pemantle and Y. Peres). Ann. Probab. 26, (1998), 4065--4087.
  69. The Number of Infinite Clusters in Dynamical Percolation.(Y. Peres and J. E. Steif).  Probab. Th. Rel. Fields. 111, (1998), 141--165.
  70. Paths with exponential intersection tails and oriented percolation. (I. Benjamini, R. Pemantle and Y. Peres) Wisconsin Math 97/RP-1h.
  71. No directed fractal percolation in zero area (L. Chayes, R. Pemantle and Y. Peres) J. Stat. Phys. 88, (1997), 1353--1362.

    We consider the fractal percolation process on the unit square, with fixed decimation parameter N and level dependent retention parameters {p_k}; that is, for all k>0, at the k`th stage every retained square of side-length N^{1-k} is partitioned into N^2 congruent subsquares, and each of these is retained with probability p_k, independently of all others. We show that if the infinite product of p_k equals 0 (i.e., if the area of the limiting set vanishes a.s.) then a.s. the limiting set contains no directed paths (that move only up, down and to the right) crossing the unit square from left to right.

  72. Bi-invariant sets and measures have integer Hausdorff dimension. (D. Meiri and Y. Peres) Erg. Th. Dynam. Sys. 19 (1999), 523--534.
  73. Self-similar measures and intersections of Cantor sets. (Y. Peres and B. Solomyak.) Trans. Amer. Math. Soc. 350 (1998) 4065--4087.
  74. Absolute Continuity of Bernoulli Convolutions, A Simple Proof , (Y. Peres and B. Solomyak.) Math. Research Letters. 3 (1996) 231-236. The distribution of a power series with random signs has been studied by many authors since the two seminal papers by Erd&oumls in 1939 and 1940. These distributions arise in several problems in dynamical systems and Hausdorff dimension estimation. A recent paper by B. Solomyak in Annals of Math. proves a conjecture made by Garsia in 1962, that these measures are absolutely continuous for almost every value of the parameter between 1/2 and 1. Here we give a considerably simplified proof of this theorem, using differentiation of measures instead of Fourier transform methods.
  75. Dynamical Percolation. Ann. IHP Probab. et. Statist. 33, (1997), 497-528. (O. Haggstrom, Y. Peres and J. E. Steif).

    We study bond percolation evolving in time where the edges turn on and off independently according to a continuous time stationary 2-state Markov chain. We construct graphs which do not percolate at criticality for a.e. time t , but do percolate for some exceptional t . (This cannot happen for noncritical percolation.) We show that for the cubical lattices in dimensions 19 and higher, at criticality there is a.s. no infinite open cluster for all t . We give a sharp criterion for a general tree to have an infinite open cluster for some t , in terms of the effective conductance of the tree.

  76. The dimension of the Brownian frontier is greater than 1. (C. J. Bishop, P. Jones, R. Pemantle and Y. Peres). (Big Postscript file.) J. Functional Analysis, 143(2), (1997), 309-336. Consider a planar Brownian motion run for a finite time. The frontier is the boundary of the unbounded component of the complement of the path. We show that the Hausdorff dimension of the frontier is strictly greater than 1. (This dimension is conjectured to be 4/3.) The proof uses a self-similar fractal tiling of the plane by "Gosper Islands", and Peter Jones's "Traveling Salesman Theorem". (Pictures due to Chris Bishop ).
  77. Ladder heights, Gaussian random walks and the Riemann zeta function. (J. Chang and Y. Peres). Ann. Probab. 25, (1997), 787-802.
  78. Random walks on the Lamplighter Group. (R. Lyons, R. Pemantle and Y. Peres). Ann. Probab., 24, (1996), 1993-2006.

    Kaimanovich and Vershik described certain finitely generated groups of exponential growth such that simple random walk on their Cayley graph escapes from the identity at a sublinear rate, or equivalently, all bounded harmonic functions on the Cayley graph are constant. Here we focus on a key example, called $G_1$ by Kaimanovich and Vershik, and show that inward-biased random walks on $G_1$ move outward faster than simple random walk. Indeed, they escape from the identity at a linear rate provided that the bias parameter is smaller than the growth rate of $G_1$. These walks can be viewed as random walks interacting with a dynamical environment on $\Z$. The proof uses potential theory to analyze a stationary environment as seen from the moving particle.

  79. Cutpoints and exchangeable events for random walks. (N. James and Y. Peres). Theory of Probab. and its Applications (Moscow), 41(4), (1996), 854-868.
  80. Packing dimension and Cartesian products. (C. J. Bishop and Y. Peres). Trans. Amer. Math. Soc. 348 (1996), 4433-4445.
  81. Points of increase for random walks. Israel J. of Math. 95 (1996), 341-347.
  82. The trace of spatial Brownian motion is capacity-equivalent to the unit square. (R. Pemantle, Y. Peres and J. Shapiro). Probab. Theory and Related Fields, 106 (1996), 379-399.
  83. Biased random walks on Galton-Watson trees. (R. Lyons, R. Pemantle and Y. Peres). Probab. Theory and Related Fields , 106 (1996), 249-264.

    We consider random walks with a bias toward the root on the family tree $T$ of a supercritical Galton-Watson branching process and show that the speed is positive whenever the walk is transient. The corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary. When the bias is directed away from the root and the extinction probability is positive, the speed may be zero even though the walk is transient; the critical bias for positive speed is determined.

  84. Tail estimates for one-dimensional random walk in random environment. (A. Dembo, Y. Peres and O. Zeitouni). Comm. Math. Phys. 181 (1996), 667-683.
  85. Hausdorff dimensions of sofic affine-invariant sets. (R. Kenyon and Y. Peres). Israel J. Math. 94 (1996), 157-168.
  86. Invariant measures of full dimension for some expanding maps. (D. Gatzouras and Y. Peres). Ergodic Theory Dynamical Syst. 17 (1997),147-167.
  87. Measures of full dimension on affine-invariant sets. (R. Kenyon and Y. Peres). Ergodic Theory Dynamical Syst. 16 (1996), 307-323.
  88. Ergodic theory on Galton-Watson trees : Speed of random walk and dimension of harmonic measure. (With R. Lyons and R. Pemantle). Ergodic Theory Dynamical Syst. 15 (1995), 593-619.

    We consider simple random walk on the family tree $T$ of a nondegenerate supercritical Galton-Watson branching process and show that the resulting harmonic measure has a.s. strictly smaller Hausdorff dimension than that of the whole boundary of $T$. Concretely, this implies that an exponentially small fraction of the $n$th level of $T$ carries most of the harmonic measure. First order asymptotics for the rate of escape, Green function and the Avez entropy of the random walk are also determined. Ergodic theory of the shift on the space of random walk paths on trees is the main tool; the key observation is that iterating the transformation induced from this shift to the subset of ``exit points'' yields a nonintersecting path sampled from harmonic measure.

  89. Conceptual proofs of L log L criteria for mean behaviour of branching processes. (R. Lyons, R. Pemantle and Y. Peres). Ann. Probab. 23 (1995), 1125-1138.

    The Kesten-Stigum Theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an $L \log L$ condition is decisive. In critical and subcritical cases, results of Kolmogorov and later authors give the rate of decay of the probability that the process survives at least $n$ generations. We give conceptual proofs of these theorems based on comparisons of Galton-Watson measure to another measure on the space of trees. This approach also explains Yaglom's exponential limit law for conditioned critical branching processes via a simple characterization of the exponential distribution.

  90. A conceptual proof of the Kesten-Stigum theorem for multi-type branching processes. (T. G. Kurtz, R. Lyons, R. Pemantle and Y. Peres) Classical and Modern Branching Processes, K. Athreya and P. Jagers (editors), Springer, New York (1996), 181-186.
  91. Martin capacity for Markov chains. (I. Benjamini, R. Pemantle and Y. Peres). Ann. Probab. 23 (1995), 1332-1346.
  92. Random walks in varying dimensions. (I. Benjamini, R. Pemantle and Y. Peres). Jour. Theoretical Probab. 9 (1996), 231-244.
  93. Galton-Watson trees with the same mean have the same polar sets. (R. Pemantle and Y. Peres). Ann. Probab. 23 (1995), 1102-1124.
  94. Critical random walk in random environment on trees. (R. Pemantle and Y. Peres). Ann. Probab. 23 (1995),105-140.
  95. Planar first-passage percolation times are not tight. (R. Pemantle and Y. Peres).  Probability and Phase Transition, G. Grimmett Editor, 261 - 264 (1994).
  96. Domination between trees and application to an explosion problem. (R. Pemantle and Y. Peres). Ann. Probab. 22 (1994), 180-194.
  97. On which graphs are all random walks in random environments transient?. (R. Pemantle and Y. Peres). Random Discrete Structures, IMA Volume 76 , (1996), D. Aldous and R. Pemantle (Editors), Springer-Verlag.
  98. Self-affine carpets on the square lattice. (I. Hueter and Y. Peres). Combinatorics, Probab. and Computing, 6, (1997) 197-204.
  99. Tree-indexed random walks on groups and first passage percolation. (I. Benjamini and Y. Peres). Probab. Theory Rel. Fields. 98 (1994), 91-112.
  100. The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure.(Y. Peres). Math. Proc. Camb. Phil. Soc. 116 (1994), 513-526.
  101. The packing measure of self-affine carpets.(Y. Peres). Math. Proc. Camb. Phil. Soc. 115 (1994), 437-450.
  102. A topological criterion for hypothesis testing (A. Dembo and Y. Peres). Ann. Stat. 22, (1994), 106--117.
  103. Uniform dilations  (N. Alon and Y. Peres). Geometric and Functional Analysis, 2, no. 1 (1992), 1-28.
  104. Iterating von Neumann's procedure for extracting random bits. (Y. Peres).  Ann. Stat. 20, (1992), 590--597.

Research of Y. Peres supported in part by NSF grants 9404391, 9803597, 0104073 and 0244479.