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| HAL : hal-00339394, version 3 |
| arXiv : 0811.2782 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (17-11-2008) | v2 (27-04-2009) | v3 (03-03-2010) |
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| Brunet-Derrida behavior of branching-selection particle systems on the line |
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| Jean Bérard 1Jean-Baptiste Gouéré 2 |
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| (17/11/2008) |
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| 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. |
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| 1 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées de Lyon |
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| 2 : | Mathématiques et Applications, Physique Mathématique d'Orléans (MAPMO) |
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CNRS : UMR6628 – Université d'Orléans |
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| Domaine | : | Mathématiques/Probabilités |
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| hal-00339394, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00339394 | |
| oai:hal.archives-ouvertes.fr:hal-00339394 | |
| Contributeur : Jean Bérard | |
| Soumis le : Mercredi 3 Mars 2010, 15:14:10 | |
| Dernière modification le : Mercredi 3 Mars 2010, 15:16:17 | |
