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

2016/07/19 by Bastien Mallein, Mallein, Bastien
Decision Sciences · Mathematics · #Markov Chains and Monte Carlo Methods #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1607.05501

arxiv created 2016/07/19 · arxiv updated 2016/07/20

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 - (1)/(2) log n converges in law toward a shifted Gumbel distribution.

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