# Brunet-Derrida behavior of branching-selection particle systems on the line

Abstract : We consider a class of branching-selection particle systems on $\R$ similar to the one considered by E. Brunet and B. Derrida in their 1997 paper "Shift in the velocity of a front due to a cutoff". Based on numerical simulations and heuristic arguments, Brunet and Derrida showed that, as the population size $N$ of the particle system goes to infinity, the asymptotic velocity of the system converges to a limiting value at the unexpectedly slow rate $(\log N)^{-2}$. In this paper, we give a rigorous mathematical proof of this fact, for the class of particle systems we consider. The proof makes use of ideas and results by R. Pemantle, and by N. Gantert, Y. Hu and Z. Shi, and relies on a comparison of the particle system with a family of $N$ independent branching random walks killed below a linear space-time barrier.
Type de document :
Article dans une revue
Communications in Mathematical Physics, Springer Verlag, 2010, 298 (2), pp.323-342
Domaine :

https://hal.archives-ouvertes.fr/hal-00339394
Contributeur : Jean Bérard <>
Soumis le : mercredi 3 mars 2010 - 15:14:10
Dernière modification le : lundi 2 mai 2016 - 09:44:12
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 18:16:41

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### Identifiants

• HAL Id : hal-00339394, version 3
• ARXIV : 0811.2782

### Citation

Jean Bérard, Jean-Baptiste Gouéré. Brunet-Derrida behavior of branching-selection particle systems on the line. Communications in Mathematical Physics, Springer Verlag, 2010, 298 (2), pp.323-342. <hal-00339394v3>

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