F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system
arXiv:1904.00082
Abstract
We study a particle system with the following diffusion-branching-selection mechanism. Particles perform independent one dimensional Brownian motions 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.
arXiv comment17 pages
References in corpus (6)
- Shift in the velocity of a front due to a cut-off
- Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization
- Noisy traveling waves: effect of selection on genealogies
- Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations
- Exact solution and precise asymptotics of a Fisher-KPP type front
- Global existence for a free boundary problem of Fisher-KPP type