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A N-branching random walk with random selection

Abstract : We consider an exactly solvable model of branching random walk with random selection, describing the evolution of a fixed number N of individuals in the real line. At each time step t → t + 1, the individuals reproduce independently at random making children around their positions and the N individuals that form the (t + 1)th generation are chosen at random among these children according to the Gibbs measure at temperature β. We compute the asymptotic speed and the genealogical behaviour of the system.
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Contributor : Bastien Mallein <>
Submitted on : Friday, May 27, 2016 - 11:16:58 AM
Last modification on : Friday, June 12, 2020 - 11:02:06 AM
Document(s) archivé(s) le : Sunday, August 28, 2016 - 10:20:17 AM


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  • HAL Id : hal-01322468, version 1
  • ARXIV : 1605.03401


Aser Cortines, Bastien Mallein. A N-branching random walk with random selection. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2017, 14 (1), pp.117--137. ⟨hal-01322468⟩



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