692 articles – 286 Notices  [english version]
 HAL : hal-00335803, version 3
 arXiv : 0810.5567
 Versions disponibles : v1 (30-10-2008) v2 (02-11-2008) v3 (06-11-2008)
 An example of Brunet-Derrida behavior for a branching-selection particle system on $\Z$
 (30/10/2008)
 We consider a branching-selection particle system on $\Z$ with $N \geq 1$ particles. During a branching step, each particle is replaced by two new particles, whose positions are shifted from that of the original particle by independently performing two random walk steps according to the distribution $p \delta_{1} + (1-p) \delta_{0}$, from the location of the original particle. During the selection step that follows, only the $N$ rightmost particles are kept among the $2N$ particles obtained at the branching step, to form a new population of $N$ particles. After a large number of iterated branching-selection steps, the displacement of the whole population of $N$ particles is ballistic, with deterministic asymptotic speed $v_{N}(p)$. As $N$ goes to infinity, $v_{N}(p)$ converges to a finite limit $v_{\infty}(p)$. The main result is that, for every \$0
 1 : Institut Camille Jordan (ICJ) CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon
 Domaine : Mathématiques/Probabilités
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 hal-00335803, version 3 http://hal.archives-ouvertes.fr/hal-00335803 oai:hal.archives-ouvertes.fr:hal-00335803 Contributeur : Jean Bérard <> Soumis le : Jeudi 6 Novembre 2008, 12:17:05 Dernière modification le : Jeudi 6 Novembre 2008, 20:12:18