Variable speed symmetric random walk driven by symmetric exclusion
Probability
2021-07-20 v1
Abstract
We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of the random walk in a balanced random environment, for which the weak quenched limit is constructed as a function of the invariant measure of the environment viewed from the walk. We bypass the need to show the existence of this invariant measure. Instead, we find the limit of the quadratic variation of the walk and give an explicit formula for it.
Cite
@article{arxiv.2107.08235,
title = {Variable speed symmetric random walk driven by symmetric exclusion},
author = {Otávio Menezes and Jonathon Peterson and Yongjia Xie},
journal= {arXiv preprint arXiv:2107.08235},
year = {2021}
}
Comments
12 pages