A limit theorem for a random walk in a stationary scenery coming from a hyperbolic dynamical system

Francoise Pene

A limit theorem for a random walk in a stationary scenery coming from a hyperbolic dynamical system

Dynamical Systems 2007-05-23 v1

Authors: Francoise Pene

Abstract

In this paper, we extend a result of Kesten and Spitzer (1979). Let us consider a stationary sequence $(\xi\_k:=f(T^k(.)))\_k$ given by an invertible probability dynamical system and some centered function $f$ . Let $(S\_n)\_n$ be a simple symmetric random walk on $Z$ independent of $(\xi\_k)\_k$ . We give examples of partially hyperbolic dynamical systems and of functions $f$ such that $n^{-3/4}(\xi(S\_1)+...+\xi(S\_k))$ converges in distribution as $n$ goes to infinity.

Keywords

random walk in random environment random walks random walk on graphs

Cite

@article{arxiv.math/0601735,
  title  = {A limit theorem for a random walk in a stationary scenery coming from a hyperbolic dynamical system},
  author = {Francoise Pene},
  journal= {arXiv preprint arXiv:math/0601735},
  year   = {2007}
}

Comments

18 pages

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