Maximal displacement in a branching random walk through interfaces
Probability
2017-06-13 v3
Abstract
In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains constant. We prove that the asymptotic behaviour of the maximal displacement in this process consists of a first ballistic order, given by the solution of an optimization problem under constraints, a negative logarithmic correction, plus stochastically bounded fluctuations.
Cite
@article{arxiv.1305.6201,
title = {Maximal displacement in a branching random walk through interfaces},
author = {Bastien Mallein},
journal= {arXiv preprint arXiv:1305.6201},
year = {2017}
}
Comments
42 pages, 7 figures, article updated to correct a mistake in the proof of Lemma 3.6