Random walk in Markovian environment

Abstract

We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on ${\mathbb{Z}}^d$. We assume that the transition probabilities of the walk depend not too strongly on the environment and that the evolution of the environment is Markovian with strong spatial and temporal mixing properties.

Published in at http://dx.doi.org/10.1214/07-AOP369 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• An almost sure invariance principle for random walks in a space-time random environment
• Random Walk in Dynamic Markovian Random Environment

Cited by in corpus (11)

• Random walks in dynamic random environments: A transference principle
• Heat conduction and Fourier's law in a class of many particle dispersing billiards
• Energy transfer in a fast-slow Hamiltonian system
• Random walk driven by the simple exclusion process
• Limit theory for random walks in degenerate time-dependent random environments
• Random walks in space time mixing environments
• Continuity and anomalous fluctuations in random walks in dynamic random environments: numerics, phase diagrams and conjectures
• A local limit theorem for a transient chaotic walk in a frozen environment
• Random walk on a perturbation of the infinitely-fast mixing interchange process
• An invariance principle for one-dimensional random walks in degenerate dynamical random environments
• Random walk in a birth-and-death dynamical environment