Weak convergence for the minimal position in a branching random walk: a simple proof

Abstract

Consider the boundary case in a one-dimensional super-critical branching random walk. It is known that upon the survival of the system, the minimal position after $n$ steps behaves in probability like $\frac{3}{2}\log n$ when $n\to \infty$. We give a simple and self-contained proof of this result, based exclusively on elementary properties of sums of i.i.d. real-valued random variables.

corrected reference in introduction

References in corpus (1)

• The critical random barrier for the survival of branching random walk with absorption