Survival probability of the branching random walk killed below a linear boundary

TL;DR

This paper provides an alternative proof for the asymptotic survival probability of a branching random walk constrained by a linear boundary, focusing on binary branching and bounded steps, with links to stochastic front theories.

Contribution

It offers a new proof approach for a known result, specifically for binary branching and bounded steps, connecting it to stochastic front models.

Findings

Survival probability asymptotics for branching random walks with linear killing boundary

Alternative proof method for existing results

Discussion of connections to Brunet-Derrida stochastic front theory

Abstract

We give an alternative proof of a result by N. Gantert, Y. Hu and Z. Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and bounded random walk steps. Connections with the Brunet-Derrida theory of stochastic fronts are discussed.