Phenomenological picture of fluctuations in branching random walks
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 correction to the average position of the rightmost particle of a branching random walk for large times , 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.
Keywords
Cite
@article{arxiv.1404.5500,
title = {Phenomenological picture of fluctuations in branching random walks},
author = {A. H. Mueller and S. Munier},
journal= {arXiv preprint arXiv:1404.5500},
year = {2014}
}
Comments
32 pages, 6 figures. v2: one Appendix added to provide more calculation details, misprints corrected, figure layout improved. To appear in Phys.Rev.E