Convergence in law of the maximum of nonlattice branching random walk

2014/04/13 by Bramson, Maury, Ding, Jian, Zeitouni, Ofer · 4 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1404.3423

Abstract

Let η^*_n denote the maximum, at time n, of a nonlattice one-dimensional branching random walk η_n possessing (enough) exponential moments. In a seminal paper, Aidekon demonstrated convergence of η^*_n in law, after recentering, and gave a representation of the limit. We give here a shorter proof of this convergence by employing reasoning motivated by Bramson, Ding and Zeitouni. Instead of spine methods and a careful analysis of the renewal measure for killed random walks, our approach employs a modified version of the second moment method that may be of independent interest.

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