Branching Random Walks in Time Inhomogeneous Environments

2011/12/05 by Ofer Zeitouni, Zeitouni, Ofer, Ming Fang +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1112.1113

arxiv created 2011/12/05 · openalex publication_date 2011/12/05 · arxiv updated 2011/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 O_P(1) (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.

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