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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.'
author:
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    A. H. Mueller${}^1$, S. Munier${}^2$[^1]\
    \
    *${}^{(1)}$Department of Physics, Columbia University, New York, USA\
    *${}^{(2)}$Centre de physique théorique, École Polytechnique, CNRS, Palaiseau, France.**
title: '**Phenomenological picture of fluctuations in branching random walks**'
---

Introduction
============

The goal of this work is to better understand the distribution of the particles generated by a branching random walk process after some large evolution time.\
Our initial motivation for addressing this problem comes from particle physics [@Iancu:2004es] (for a review, see [@Munier:2009pc]). In the context of the scattering of hadrons at large energies, high-occupation quantum fluctuations dominate some of the 