Random walks and branching processes in correlated Gaussian environment
Probability
2016-12-21 v1 Disordered Systems and Neural Networks
Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr. From the persistence results, we can deduce properties of critical branching processes with offspring sizes geometrically distributed with correlated random parameters. More precisely, we obtain estimates on the tail distribution of its total population size, of its maximum population, and of its extinction time.
Keywords
Cite
@article{arxiv.1607.00999,
title = {Random walks and branching processes in correlated Gaussian environment},
author = {Frank Aurzada and Alexis Devulder and Nadine Guillotin-Plantard and Françoise Pène},
journal= {arXiv preprint arXiv:1607.00999},
year = {2016}
}