EPL Association, European Physical Society Letters, 6(87), p. 60010, 2009
DOI: 10.1209/0295-5075/87/60010
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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. ; Comment: 4 pages, 2 figures