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

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

2010-06-07

arxiv.org/abs/1006.1266v2

Period. Math. Hungar. (special issue in honour of E. Cs\'aki and P.R\'ev\'esz) (2010), 61,43-54

Mathematics

Probability

corrected reference in introduction

Scientific paper

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 ${3\over 2} \log n$ 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.

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