TY - JOUR
T1 - Phenomenological picture of fluctuations in branching random walks
AU - Mueller, A. H.
AU - Munier, S.
N1 - Publisher Copyright:
© 2014 American Physical Society.
PY - 2014/10/30
Y1 - 2014/10/30
N2 - 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/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.
AB - 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/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.
U2 - 10.1103/PhysRevE.90.042143
DO - 10.1103/PhysRevE.90.042143
M3 - Article
AN - SCOPUS:84913558317
SN - 1539-3755
VL - 90
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
M1 - 042143
ER -