A Branching Random Walk Seen from the Tip View Full Text


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Article Info

DATE

2011-05

AUTHORS

Éric Brunet, Bernard Derrida

ABSTRACT

We show that all the time-dependent statistical properties of the rightmost points of a branching Brownian motion can be extracted from the traveling wave solutions of the Fisher-KPP equation. The distribution of all the distances between the rightmost points has a long time limit which can be understood as the delay of the Fisher-KPP traveling waves when the initial condition is modified. The limiting measure exhibits the surprising property of superposability: the statistical properties of the distances between the rightmost points of the union of two realizations of the branching Brownian motion shifted by arbitrary amounts are the same as those of a single realization. We discuss the extension of our results to more general branching random walks. More... »

PAGES

420

References to SciGraph publications

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  • 2007-03. Spin Glass Computations and Ruelle’s Probability Cascades in JOURNAL OF STATISTICAL PHYSICS
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