IC   26529
INSTITUTO DE CALCULO REBECA CHEREP DE GUBER
Unidad Ejecutora - UE
artículos
Título:
F-KPP Scaling limit and selection principlefor a Brunet-Derrida type particle system
Autor/es:
PABLO GROISMAN; MARTÍNEZ JULIÁN; MATTHIEU JONCKHEERE
Revista:
ALEA
Editorial:
IMPA
Referencias:
Lugar: Rio de Janeiro; Año: 2019 vol. XVII p. 589 - 607
ISSN:
1517-106X
Resumen:
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.