An exponential estimate for the extinction time of the branching random walk on a cube

Abstract

We prove the exponential estimate \begin{equation*} P \{ s < τ< \infty \} \leq C e^{-q s}, \quad s \geq 0, \end{equation*} where $C,q>0$ are constants and $\tau$ is the extinction time of the supercritical branching random walk (BRW) on a cube. We cover both the discrete-space and continuous-space BRWs.

11 pages; minor text modifications only in the updated version, no essential changes

References in corpus (1)

• Branching random walks and multi-type contact-processes on the percolation cluster of ${\mathbb{Z}}^d$