A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space.
A remark concerning random walks with random potentials
We consider random walks where each path is equipped with a random weight which is stationary and independent in space and time. We show that under some assumptions the arising probability distributions are in a sense uniformly absolutely continuous with respect to the usual probability distribution for symmetric random walks.
A remark on the norm of a random walk on surface groups
We show that the norm of the random walk operator on the Cayley graph of the surface group in the standard presentation is bounded by 1/√g where g is the genus of the surface.
A Remark on the Strong Law of Large Numbers.
A Sharper Form of the Doeblin-Lévy-Kolmogorov-Rogozin Inequality for Concentration Functions.
A special set of exceptional times for dynamical random walk on .
A survey of random processes with reinforcement.
A Theorem on Convergence to a Lévy Process.
A weighted pointwise ergodic theorem
About the generating function of a left bounded integer-valued random variable
We give a relation between the sign of the mean of an integer-valued, left bounded, random variable and the number of zeros of inside the unit disk, where is the generating function of , under some mild conditions
Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
We consider transient one-dimensional random walks in a random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of “valleys“ of height . In the quenched setting, we also sharply estimate the distribution of the walk at time .
Agrégation limitée par diffusion interne sur Zd
Almost everywhere convergence of convolution powers on compact abelian groups
It is well-known that a probability measure on the circle satisfies for every , every (some) , if and only if for every non-zero ( is strictly aperiodic). In this paper we study the a.e. convergence of for every whenever . We prove a necessary and sufficient condition, in terms of the Fourier–Stieltjes coefficients of , for the strong sweeping out property (existence of a Borel set with a.e. and a.e.). The results are extended to general compact Abelian groups with Haar...
Almost Everywhere Convergence of Series.
Almost sure absolute continuity of Bernoulli convolutions
We prove an extension of a result by Peres and Solomyak on almost sure absolute continuity in a class of symmetric Bernoulli convolutions.
Amenability of linear-activity automaton groups
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.
Amenability, unimodularity, and the spectral radius of random walks on finite graphs.
An almost sure central limit theorem for independent random variables
An analog of Wald's identity for random walks with infinite mean.
An Application of the Renewal Theoretic Selection Principle: The First Divisible Sum.