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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2020

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.

Dates et versions

hal-03625700 , version 1 (31-03-2022)

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Pablo Groisman, Matthieu Jonckheere, Julián Martínez. F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2020, 17 (1), pp.589. ⟨10.30757/ALEA.v17-23⟩. ⟨hal-03625700⟩
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