Branching random walk in random environment

Xinxin Chen; Chenlin Gu; Zhiqi Zhao

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arXiv · 2608.13084

Branching random walk in random environment

Xinxin Chen·Chenlin Gu·Zhiqi Zhao

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Abstract

We consider a branching random walk on $\Z^d$ in a random environment given by Bernoulli site percolation with parameter $p\in (0,1)$. In this model, each particle located at an open site reproduces according to a law $\mu_\circ$, whereas a particle at a closed site reproduces according to another law $\mu_\bullet$. Each newly born child performs an independent simple random walk jump from the position of its parent. We study the quenched survival probability under various assumptions on $(\mu_\circ, \mu_\bullet)$ and establish a Yaglom theorem when both offspring distributions are critical.

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Xinxin Chen, Chenlin Gu, Zhiqi Zhao. 2026-08-13. Branching random walk in random environment. https://arxiv.org/abs/2608.13084

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