Statistics at the tip of a branching random walk and the delay of traveling waves

Details Statistics at the tip of a branching random walk and the delay of traveling waves Statistics at the tip of a branching random walk and the delay of traveling waves

2009-05-05

arxiv.org/abs/0905.0613v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 2 figures

Scientific paper

We study the limiting distribution of particles at the frontier of a branching random walk. The positions of these particles can be viewed as the lowest energies of a directed polymer in a random medium in the mean-field case. We show that the average distances between these leading particles can be computed as the delay of a traveling wave evolving according to the Fisher-KPP front equation. These average distances exhibit universal behaviors, different from those of the probability cascades studied recently in the context of mean field spin-glasses.

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