Branching Random Walks in Time Inhomogeneous Environments

Details Branching Random Walks in Time Inhomogeneous Environments Branching Random Walks in Time Inhomogeneous Environments

2011-12-05

arxiv.org/abs/1112.1113v1

Mathematics

Probability

Scientific paper

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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