A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts

TL;DR

This paper develops a phenomenological theory to predict the full statistical behavior of the position of fluctuating pulled fronts under weak noise, aligning well with numerical simulations.

Contribution

It introduces a parameter-free analytical framework for the velocity, diffusion constant, and cumulants of fluctuating fronts in the Fisher-KPP class.

Findings

Analytical predictions match numerical simulations

Provides full statistics of front position under noise

Offers insights into the diffusion mechanism of pulled fronts

Abstract

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 travelling 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.