On the tail of the branching random walk local time

Omer Angel; Tom Hutchcroft; Antal A. Járai

On the tail of the branching random walk local time

Probability 2020-02-28 v1

Authors: Omer Angel , Tom Hutchcroft , Antal A. Járai

Abstract

Consider a critical branching random walk on $\mathbb{Z}^d$ , $d\geq 1$ , started with a single particle at the origin, and let $L(x)$ be the total number of particles that ever visit a vertex $x$ . We study the tail of $L(x)$ under suitable conditions on the offspring distribution. In particular, our results hold if the offspring distribution has an exponential moment.

Keywords

branching random walk local time tail behavior offspring distribution exponential moment critical case

Cite

@article{arxiv.2002.12188,
  title  = {On the tail of the branching random walk local time},
  author = {Omer Angel and Tom Hutchcroft and Antal A. Járai},
  journal= {arXiv preprint arXiv:2002.12188},
  year   = {2020}
}

Comments

28 pages

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