Geodesic
$N$-Branching random~walk with $\alpha$-stable spine
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 365-392

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We consider a branching-selection particle system on the real line, introduced by Brunet and Derrida in [Phys. Rev. E, 56 (1997), pp. 2597–2604]. 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 [Comm. Math. Phys., 298 (2010), pp. 323–342], assuming the tails of the displacement decays at exponential rate; Bérard and Maillard [Electron. J. Probab., 19 (2014), 22] 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 $\alpha$-stable random walk.
Keywords: branching random walk, selection
Mots-clés : stable distribution. 
@article{TVP_2017_62_2_a6,
     author = {B. Mallein},
     title = {$N${-Branching} random~walk with $\alpha$-stable spine},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {365--392},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a6/}
}
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B. Mallein. $N$-Branching random~walk with $\alpha$-stable spine. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 365-392. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a6/