Non-perturbative approach to random walk in markovian environment

TL;DR

This paper establishes an averaged central limit theorem for a random walk in a Markovian environment, where each site’s environment evolves independently as a Markov chain, advancing understanding of stochastic processes in dynamic settings.

Contribution

It introduces a non-perturbative method to prove an averaged CLT for random walks in environments composed of independent Markov chains, extending previous results.

Findings

Proves an averaged CLT for the model.

Demonstrates the applicability of non-perturbative techniques.

Provides a rigorous mathematical framework for dynamic environments.

Abstract

We prove an averaged CLT for a random walk in a dynamical environment where the states of the environment at different sites are independent Markov chains.