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A $N$-branching random walk with random selection
Aser Cortines, Bastien Mallein · 2016-05-11 · via math.PR updates on arXiv.org

We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its offspring are positioned around its current locations. Among all children, $N$ individuals are sampled at random without replacement to form the next generation, such that an individual at position $x$ is chosen with probability proportional to $\mathrm{e}^{βx}$. We compute the asymptotic speed and the genealogical behavior of the system.

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