A short proof of the asymptotic of the minimum of the branching random walk after time $n$

Bastien Mallein

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arXiv · 1607.05501

A short proof of the asymptotic of the minimum of the branching random walk after time $n$

Bastien Mallein

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Abstract

We write $R_n$ for the minimal position attained after time $n$ by a branching random walk in the boundary case. In this article, we prove that $R_n - \frac{1}{2} \log n$ converges in law toward a shifted Gumbel distribution.

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Bastien Mallein. 2016-07-19. A short proof of the asymptotic of the minimum of the branching random walk after time $n$. https://arxiv.org/abs/1607.05501

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