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arXiv · 1404.5500

Phenomenological picture of fluctuations in branching random walks

A. H. Mueller·S. Munier
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Abstract

We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the $1/\sqrt{t}$ correction to the average position of the rightmost particle of a branching random walk for large times $t\gg 1$, computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of branching random walk.

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A. H. Mueller, S. Munier. 2014-10-22. Phenomenological picture of fluctuations in branching random walks. https://doi.org/10.1103/physreve.90.042143

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