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arXiv · 2002.12188

On the tail of the branching random walk local time

Omer Angel·Tom Hutchcroft·Antal A. Járai
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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.

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Omer Angel, Tom Hutchcroft, Antal A. Járai. 2020-02-27. On the tail of the branching random walk local time. https://arxiv.org/abs/2002.12188

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