Branching Random Walks in Time Inhomogeneous Environments
Probability
2011-12-07 v1
Abstract
We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change over time macroscopically. We find the asymptotics of the maximum up to an (stochastically bounded) error, and focus on the following phenomena: the profile of the variance matters, both to the leading (velocity) term and to the logarithmic correction term, and the latter exhibits a phase transition.
Cite
@article{arxiv.1112.1113,
title = {Branching Random Walks in Time Inhomogeneous Environments},
author = {Ofer Zeitouni and Ming Fang},
journal= {arXiv preprint arXiv:1112.1113},
year = {2011}
}