A $N$-branching random walk with random selection

Aser Cortines, Bastien Mallein

Published 2016-05-11Version 1

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 $t\to t\!+\!1$, 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 $\beta$. We compute the asymptotic speed and the genealogical behaviour of the system.