Non-trivial linear bounds for a random walk driven by a simple symmetric exclusion process

TL;DR

This paper establishes significant linear bounds on the displacement of a random walk influenced by a one-dimensional symmetric exclusion process, using advanced multiscale renormalization techniques.

Contribution

It introduces novel linear bounds for a random walk in a dynamic environment driven by a symmetric exclusion process, adapting multiscale renormalization methods.

Findings

Linear bounds for the displacement of the random walk

Application of multiscale renormalization methods

Enhanced understanding of random walks in dynamic environments

Abstract

Non-trivial linear bounds are obtained for the displacement of a random walk in a dynamic random environment given by a one-dimensional simple symmetric exclusion process in equilibrium. The proof uses an adaptation of multiscale renormalization methods of Kesten and Sidoravicius.