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We prove the exponential estimate  \begin{equation*}  P \{ s < \tau < \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 thesupercritical branching random walk (BRW) on a cube. We cover both thediscrete-space and continuous-space BRWs.

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