Branching random walk in random environment

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 \(μ_\circ\), whereas a particle at a closed site reproduces according to another law \(μ_\bullet\). 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 \((μ_\circ, μ_\bullet)\) and establish a Yaglom theorem when both offspring distributions are critical.

40 pages, 1 figure with 2 panels