Asymptotic of the maximal displacement in a branching random walk
Probability
2019-05-21 v1
Abstract
In this article, we study the maximal displacement in a branching random walk. We prove that its asymptotic behaviour consists in a first almost sure ballistic term, a negative logarithmic correction in probability and stochastically bounded fluctuations. This result, proved by Addario-Berry and Reed, and Hu and Shi is given here under close-to-optimal integrability conditions. We provide simple proofs for this result, also deducing the genealogical structure of the individuals that are close to the maximal displacement.
Keywords
Cite
@article{arxiv.1605.08292,
title = {Asymptotic of the maximal displacement in a branching random walk},
author = {Bastien Mallein},
journal= {arXiv preprint arXiv:1605.08292},
year = {2019}
}