Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts.
We propose a phenomenological description for the effect of a weak noise on the position of a front described by the Fisher-Kolmogorov-Petrovsky-Piscounov equation or any other traveling-wave equation in the same class. Our scenario is based on four hypotheses on the relevant mechanism for the diffusion of the front. Our parameter-free analytical predictions for the velocity of the front, its diffusion constant and higher cumulants of its position agree with numerical simulations.
Brunet
E
E
Laboratoire de Physique Statistique, Ecole Normale Supérieure, Paris, France.
Derrida
B
B
Mueller
A H
AH
Munier
S
S