Phenomenological picture of fluctuations in branching random walks.
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≫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 a branching random walk.
Department of Physics, Columbia University, New York, New York 10027, USA.
A H
AH
Mueller
Centre de Physique Théorique, École Polytechnique, CNRS, Palaiseau, France.
S
S
Munier