Weak quenched limit theorems for a random walk in a sparse random environment
Probability
2023-01-03 v1
Abstract
We study the quenched behaviour of a perturbed version of the simple symmetric random walk on the set of integers. The random walker moves symmetrically with an exception of some randomly chosen sites where we impose a random drift. We show that if the gaps between the marked sites are i.i.d. and regularly varying with a sufficiently small index, then there is no strong quenched limit laws for the position of the random walker. As a consequence we study the quenched limit laws in the context of weak convergence of random measures.
Cite
@article{arxiv.2301.00478,
title = {Weak quenched limit theorems for a random walk in a sparse random environment},
author = {Dariusz Buraczewski and Piotr Dyszewski and Alicja Kołodziejska},
journal= {arXiv preprint arXiv:2301.00478},
year = {2023}
}