Papers

Noise Stability of Weighted Majority
(Y. Peres).

Minimal Spanning Forests. (R.
Lyons, Y. Peres, and O. Schramm). Preprint.

Fluctuation of planar Brownian loop
capturing large area. (A. Hammond and Y. Peres).

Scaling limits of the uniform spanning
tree and looperased random walk on finite graphs. (Yuval Peres
and D. Revelle). Submitted.

Markov chains in smooth Banach spaces
and Gromov hyperbolic metric spaces. (A. Naor, Y. Peres, O.
Schramm and S. Sheffield). Preprint.

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.

Recurrent graphs where two independent
random walks collide finitely often. (M. Krishnapur and Y.
Peres). Electron. Comm. Probab. 9 (2004), 7281.

The sharp Hausdorff measure condition
for length of projections. (Y. Peres and B. Solomyak).
Proceedings Amer. Math. Soc. To appear.

Shuffling by semirandom transpositions.
(E. Mossel, Y. Peres and A. Sinclair). 45th Symposium on
Foundations of Comp. Sci. To appear.

What is the probability of intersecting
the set of Brownian double points? (R. Pemantle and Y. Peres).

Mixing times for random walks on finite
lamplighter groups. (Y. Peres and D. Revelle). Electron.
Journal Probab. 9 (2004), 82545.

Bootstrap percolation on infinite trees
and nonamenable groups. (J. Balogh, Y. Peres and G. Pete).
Combinatorics, Probability & Computing. To appear.

Zeros of the i.i.d. Gaussian power
series: a conformally invariant determinantal process. (Y. Peres
and B. Virág). Acta Math. To appear.

Fast Simulation of New Coins From Old.
(S. Nacu and Y. Peres). Annals of Applied Probability.
15, no. 1A (2005).

An invariant of finitary codes with
finite expected square root coding length. (N. Harvey and Y.
Peres). Ergodic Theory and Dynamical Systems. To appear

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),
568578.

Extra heads and invariant allocations.
(A. Holroyd and Y. Peres). The Annals of Probability. 33, no.1
(2005).

Evolving sets, mixing and heat kernel
bounds. (B. Morris and Y. Peres). Prob. Theory and
Related Fields. To appear.

On the Maximum Satisfiability of Random
Formulas. (D. Achlioptas, A. Naor and Y. Peres). Preprint.

The Threshold for Random kSAT is 2^k
ln2  O(k). (D. Achlioptas and Y. Peres). J. Amer. Math.
Soc. 17, no. 4, (2004), 947973.

Brownian intersections, cover times and
thick points via trees. (Y. Peres). Proceedings of the ICM,
Beijing 2002, vol. 3, 7378

Identifying several biased coins
encountered by a hidden random walk. (D. Levin, Y. Peres).
Rand. Struct. and Alg. 25, no. 1, (2004), 91114.

New coins from old: computing with
unknown bias. (E. Mossel and Y. Peres). Combinatorica.
To appear.

Anchored Expansion, Percolation and
Speed. (D. Chen, Y. Peres, G. Pete). Annals of
Probability 32, no. 4, (2004).

Late Points for Random Walks in Two
Dimensions. (A. Dembo, Y. Peres, J. Rosen, O. Zeitouni).
Annals of Probability. To appear.
 The speed of biased random walk on percolation clusters. (N. Berger, N.
Gantert, and Y. Peres). Probab. Theory Related Fields 126, no.
2, (2003), 221242.

Transience of percolation clusters on
wedges. (O. Angel, I. Benjamini, N. Berger and Y. Peres).
Electron. J. Probab. To appear.

Cover Times for Brownian Motion and
Random Walks in Two Dimensions. (A. Dembo, Y. Peres, J. Rosen,
and O. Zeitouni). Ann. Math., 160 (2004).

Markov Chain Intersections and the
LoopErased Walk. (R. Lyons, Y. Peres and Oded Schramm) Ann.
Inst. H. Poincar\'e Probab. Statist. 39, no. 5, (2003), 779791.

Markov chain intersections and the
looperased walk. (R. Lyons, Y. Peres and O. Schramm.) Ann. Inst.
H. Poincare Probab. Statist. 39 (2003), no. 5, 779791.
Let $X$ and $Y$ be independent transient
Markov chains on the same state space that have the same transition
probabilities. Let $L$ denote the ``looperased 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.}
 Which properties of a random sequence are dynamically sensitive? (I.
Benjamini, O. Haggstrom, Y. Peres and J. Steif). Ann. Probab. 31
no. 1 (2003), 134.

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 (d1)/4. A new notion of
stochastic dimension is introduced and used in the proof.

Information flow on trees (Elchanan
Mossel and Y. Peres). Ann. Appl Prob. 13 no. 3
(2003), 817844.
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 secretsharing protocols.

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), 29695003.

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), 473496.

Large Deviations for Random Walks on
GaltonWatson Trees: Averaging and Uncertainty. (A. Dembo, N.
Gantert, Y. Peres and O. Zeitouni). Probab. Theory Related Fields
122, no.2, (2002), 241288.

Bernoulli convolutions and an
intermediate value theorem for entropies of Kpartitions. (E.
Lindenstrauss, Y. Peres and W. Schlag). J. Anal. Math. 87,
(2002), 337367.

A large Wiener sausage from crumbs
(O. Angel, I. Benjamini and Y. Peres)
Electronic Comm. Probab. Vol.
5 (2000) Paper no. 7, pages 6771.

A dimension gap for continued fractions
with independent digits (Y. Kifer, Y. Peres and B. Weiss)
Israel J. Math. To appear.

Equivalence of positive Hausdorff
measure and the open set condition for selfconformal sets (Y.
Peres, M. Rams, K. Simon and B. Solomyak). Proc. Amer. Math. Soc.
129, no. 9, (2001), 26892699.

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.

Thick points for planar Brownian motion
and the ErdosTaylor conjecture on random walk. (A. Dembo, Y.
Peres, J. Rosen and O. Zeitouni). Acta Math. 186 no. 2,
(2001), 239270.
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 $2a$. 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 $n^{1a\pi}$.

Existence of $L^q$ dimensions and
entropy dimension for selfconformal measures. (Y. Peres and B.
Solomyak). Indiana Univ. Math. J. 49, no. 4, (2000),
16031621.
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 selfconformal
measure, without any separation assumptions. We also show the existence of
ordertwo densities for a class of selfsimilar measures with overlap.

Percolation in a dependent random
environment. (Johan Jonasson, Elchanan Mossel and Y. Peres).
Random Struct. Alg. 16, (2000), 333343.
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.)

Where did the Brownian particle go?
(with R. Pemantle, J. Pitman and M. Yor) Electron. J. Probab.
6, no. 10,22 (2001) pp. (electronic).

Approximation by polynomials with
coefficients 1, 1. (Y. Peres and B. Solomyak.) J. Number
Theory , 84, (2000), 185198.
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.

Percolation on nonamenable products at
the uniqueness threshold. (Y. Peres). Annales
Institut H. Poincare (Probab. et Stat.) 36, (2000), 395406.

Limsup random fractals. (D.
Khoshnevisan, Y. Peres and Y. Xiao).
Elect. J. Probab. Vol 5,
(2000), paper 4, 124.

Nonamenable products are not treeable.
(R. Pemantle and Y. Peres) Israel Journal of Math 118, (2000),
147155.

Selfsimilar sets of zero Hausdorff
measure and positive packing measure. (Y. Peres, K. Simon and B.
Solomyak).Israel Journal of Math. 117, pp. 353379 (2000).

Thick Points for Transient Symmetric
Stable Processes. (A. Dembo, Y. Peres, J. Rosen and O. Zeitouni).
Elect. J. Probab. 4, (1999), Paper No. 10, 113.

Broadcasting on trees and the Ising
model. (W. Evans, C. Kenyon, Y. Peres and L. Schulman).
Ann. Appl. Probab. 10, (2000), 410433.

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. 3965.

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. 6990.

Thick points for spatial Brownian
motion: multifractal analysis of occupation measure. (A. Dembo,
Y. Peres, J. Rosen and O. Zeitouni).To appear, Ann. Probab.

Crossing estimates and convergence of
Dirichlet functions along random walk and diffusion paths. (A.
Ancona, R. Lyons and Y. Peres) Ann. Probab. 27 (1999), 970989.

A phase transition in random coin
tossing. (D. Levin R. Pemantle and Y. Peres). Ann. Probab.
29 no. 4, (2001), 16371669.

Smoothness of projections, Bernoulli
convolutions and the dimension of exceptions. (Y. Peres and W.
Schlag.)Duke Math. J. 102, (2000), 193251.

Uniform spanning forests.
(With I. Benjamini, R. Lyons, Y. Peres and O. Schramm). Ann.
Probab. 29, (2001), 165.

Eventual Intersection for Sequences of
Levy Processes. (Steven N. Evans and Y. Peres).
Electronic Communications in Probability, Vol. 3 (1998) Paper no. 3, pages
2127.

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), 264278.

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),
273285.

Critical percolation on any nonamenable
group has no infinite clusters. (I. Benjamini, R. Lyons, Y. Peres
and O. Schramm.) Ann. Probab. 27, (1999), 13471356.

Entropy of Convolutions on the Circle.
(E. Lindenstrauss, D. Meiri and Y. Peres) Ann. Math. 149, (1999),
871904.
For ergodic $p$invariant measures on the
1torus $T$, 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.

Groupinvariant percolation on graphs.
(I. Benjamini, R. Lyons, Y. Peres and O. Schramm.) Geom. Func. Anal. 9
(1999), 2966.

Resistance bounds for first passage
percolation and maximum flow. (R. Lyons, R. Pemantle and Y.
Peres) J. Combin. Theory Ser. A, 86 (1999), 158168.

Intersectionequivalence of Brownian
paths and certain branching processes (Y. Peres). Comm.
Math. Phys. 177 (1996), 417434. 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:
 Classical capacity estimates for Brownian hitting probabilities;
 Russell Lyons' capacity estimates for percolation probabilities on
trees;
 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.)

Unpredictable Paths and Percolation.
(I. Benjamini, R. Pemantle and Y. Peres). Ann. Probab. 26, (1998),
40654087.

The Number of Infinite Clusters in
Dynamical Percolation.(Y. Peres and J. E. Steif).
Probab. Th. Rel. Fields. 111, (1998), 141165.

Paths with exponential intersection
tails and oriented percolation. (I. Benjamini, R. Pemantle and Y.
Peres) Wisconsin Math 97/RP1h.

No directed fractal percolation in zero
area (L. Chayes, R. Pemantle and Y. Peres) J. Stat. Phys.
88, (1997), 13531362.
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 sidelength N^{1k} 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.

Biinvariant sets and measures have
integer Hausdorff dimension. (D. Meiri and Y. Peres) Erg. Th.
Dynam. Sys. 19 (1999), 523534.

Selfsimilar measures and intersections
of Cantor sets. (Y. Peres and B. Solomyak.) Trans. Amer.
Math. Soc. 350 (1998) 40654087.

Absolute Continuity of Bernoulli
Convolutions, A Simple Proof , (Y. Peres and B. Solomyak.)
Math. Research Letters. 3 (1996) 231236. The distribution of a power
series with random signs has been studied by many authors since the two
seminal papers by Erdös 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.

Dynamical Percolation.
Ann. IHP Probab. et. Statist. 33, (1997), 497528. (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 2state 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.

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), 309336. 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 selfsimilar
fractal tiling of the plane
by
"Gosper Islands", and Peter
Jones's "Traveling Salesman Theorem". (Pictures due to Chris Bishop
).

Ladder heights, Gaussian random walks
and the Riemann zeta function. (J. Chang and Y. Peres). Ann.
Probab. 25, (1997), 787802.

Random walks on the Lamplighter Group.
(R. Lyons, R. Pemantle and Y. Peres). Ann. Probab., 24, (1996),
19932006.
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 inwardbiased 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.

Cutpoints and exchangeable events for
random walks. (N. James and Y. Peres). Theory of Probab. and
its Applications (Moscow), 41(4), (1996), 854868.

Packing dimension and Cartesian
products. (C. J. Bishop and Y. Peres). Trans. Amer. Math.
Soc. 348 (1996), 44334445.

Points of increase for random walks.
Israel J. of Math. 95 (1996), 341347.

The trace of spatial Brownian motion is
capacityequivalent to the unit square. (R. Pemantle, Y. Peres
and J. Shapiro). Probab. Theory and Related Fields, 106 (1996),
379399.

Biased random walks on GaltonWatson
trees. (R. Lyons, R. Pemantle and Y. Peres). Probab. Theory
and Related Fields , 106 (1996), 249264.
We consider random walks with a bias
toward the root on the family tree $T$ of a supercritical GaltonWatson
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.

Tail estimates for onedimensional
random walk in random environment. (A. Dembo, Y. Peres and O.
Zeitouni). Comm. Math. Phys. 181 (1996), 667683.

Hausdorff dimensions of sofic
affineinvariant sets. (R. Kenyon and Y. Peres). Israel J.
Math. 94 (1996), 157168.

Invariant measures of full dimension for
some expanding maps. (D. Gatzouras and Y. Peres). Ergodic
Theory Dynamical Syst. 17 (1997),147167.

Measures of full dimension on
affineinvariant sets. (R. Kenyon and Y. Peres). Ergodic
Theory Dynamical Syst. 16 (1996), 307323.

Ergodic theory on GaltonWatson trees :
Speed of random walk and dimension of harmonic measure. (With R.
Lyons and R. Pemantle). Ergodic Theory Dynamical Syst. 15 (1995),
593619.
We consider simple random walk on the
family tree $T$ of a nondegenerate supercritical GaltonWatson 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.

Conceptual proofs of L log L criteria
for mean behaviour of branching processes. (R. Lyons, R. Pemantle
and Y. Peres). Ann. Probab. 23 (1995), 11251138.
The KestenStigum 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 GaltonWatson
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.

A conceptual proof of the KestenStigum
theorem for multitype 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), 181186.

Martin capacity for Markov chains.
(I. Benjamini, R. Pemantle and Y. Peres). Ann. Probab. 23 (1995),
13321346.

Random walks in varying dimensions.
(I. Benjamini, R. Pemantle and Y. Peres). Jour. Theoretical Probab.
9 (1996), 231244.

GaltonWatson trees with the same mean
have the same polar sets. (R. Pemantle and Y. Peres). Ann.
Probab. 23 (1995), 11021124.

Critical random walk in random
environment on trees. (R. Pemantle and Y. Peres). Ann. Probab.
23 (1995),105140.

Planar firstpassage percolation times
are not tight. (R. Pemantle and Y. Peres). Probability
and Phase Transition, G. Grimmett Editor, 261  264 (1994).

Domination between trees and application
to an explosion problem. (R. Pemantle and Y. Peres). Ann.
Probab. 22 (1994), 180194.

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), SpringerVerlag.

Selfaffine carpets on the square
lattice. (I. Hueter and Y. Peres). Combinatorics, Probab. and
Computing, 6, (1997) 197204.

Treeindexed random walks on groups and
first passage percolation. (I. Benjamini and Y. Peres).
Probab. Theory Rel. Fields. 98 (1994), 91112.

The selfaffine carpets of McMullen and
Bedford have infinite Hausdorff measure.(Y. Peres).
Math. Proc. Camb. Phil. Soc. 116 (1994), 513526.

The packing measure of selfaffine
carpets.(Y. Peres). Math. Proc. Camb. Phil. Soc.
115 (1994), 437450.

A topological criterion for hypothesis
testing (A. Dembo and Y. Peres). Ann. Stat. 22, (1994),
106117.

Uniform dilations (N.
Alon and Y. Peres). Geometric and Functional Analysis, 2, no. 1
(1992), 128.

Iterating von Neumann's procedure for
extracting random bits. (Y. Peres). Ann. Stat.
20, (1992), 590597.
Research of Y. Peres supported
in part by NSF grants 9404391, 9803597, 0104073 and 0244479.