Work

A $N$-branching random walk with random selection

Year: 2016

Type: article

Abstract: 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.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.1605.03401

Authors: Cortines, Aser, Mallein, Bastien

Institutions: Laboratoire de Probabilités et Modèles Aléatoires, École Normale Supérieure - PSL, Département de mathématiques et applications

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4299316114

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