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.