Random Markov property for random walks in random environments
Probability
2024-09-20 v1
Abstract
We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the construction of a random field built from the environment, that has to satisfy a certain random Markov property along with some mixing estimates. We apply this criterion to correlated environments such as Boolean percolation and renewal chains featuring polynomial decay of correlations.
Cite
@article{arxiv.2409.12515,
title = {Random Markov property for random walks in random environments},
author = {Julien Allasia and Rangel Baldasso and Oriane Blondel and Augusto Teixeira},
journal= {arXiv preprint arXiv:2409.12515},
year = {2024}
}