A N-branching random walk with random selection
Résumé
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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