F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system
Résumé
We study a particle system with the following diffusion-branching-
selection mechanism. Particles perform independent one dimensional Brownian mo-
tions and on top of that, at a constant rate, a pair of particles is chosen uniformly at
random and both particles adopt the position of the rightmost one among them. We
show that the cumulative distribution function of the empirical measure converges
to a solution of the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation and
use this fact to prove that the system selects the minimal macroscopic speed as the
number of particles goes to infinity.