N -Branching random walk with α-stable spine

Abstract : We consider a branching-selection particle system on the real line, introduced by Brunet and Derrida in [7]. In this model the size of the population is fixed to a constant N. At each step individuals in the population reproduce independently, making children around their current position. Only the N rightmost children survive to reproduce at the next step. Bérard and Gouéré studied the speed at which the cloud of individuals drifts in [2], assuming the tails of the displacement decays at exponential rate; Bérard and Maillard [3] took interest in the case of heavy tail displacements. We take interest in an intermediate model, considering branching random walks in which the critical spine behaves as an α-stable random walk.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01322452
Contributeur : Bastien Mallein <>
Soumis le : lundi 30 mai 2016 - 11:17:17
Dernière modification le : jeudi 27 avril 2017 - 09:45:46
Document(s) archivé(s) le : mercredi 31 août 2016 - 10:51:37

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  • HAL Id : hal-01322452, version 1

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INSMI | UPMC | PSL | USPC | PMA

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Bastien Mallein. N -Branching random walk with α-stable spine. 2015. <hal-01322452>

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