PreprintarXiv licencearXiv
Random walk in a regenerating random environment
Abstract
In this paper we consider random walks moving in a dynamic random environment that is completely resampled with probability p after each step of the random walker. This resampling yields a straightforward regeneration structure and limit theorems, such as a law of large numbers with a limiting speed v(p) that depends on p. We investigate several properties of v(p) as a function of p, such as differentiability and monotonicity. Similarily, we study the limiting diffusivity σ2(p) in a central limit theorem.
Related
- The velocity is deterministic in random walk in 2-valued i.i.d. random environment
- Random walk in a null recurrent birth-and-death dynamical environment
- Random walk in a non-homogeneous random environment on some random trees and the non-negative integers
- Annealed Survival Probability of Random Walk in an Inhomogeneous Poisson Environment of Mobile Traps
- On the critical branching random walk I: branching capacity and visiting probability
BibTeX
@misc{martin2026random,
title = {{Random walk in a regenerating random environment}},
author = {Raphael Martin and Jan Nagel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11919},
eprint = {2610.11919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11919},
}
RIS
TY - UNPB
TI - Random walk in a regenerating random environment
AU - Raphael Martin
AU - Jan Nagel
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11919
UR - https://arxiv.org/abs/2610.11919
AB - In this paper we consider random walks moving in a dynamic random environment that is completely resampled with probability p after each step of the random walker. This resampling yields a straightforward regeneration structure and limit theorems, such as a law of large numbers with a limiting speed v(p) that depends on p. We investigate several properties of v(p) as a function of p, such as differentiability and monotonicity. Similarily, we study the limiting diffusivity σ^2(p) in a central limit theorem.
ER -