A Branching-selection process related to censored Galton-Walton processes
Olivier Couronn\'e (MODAL'X), Lucas Gerin (MODAL'X)
TL;DR
This paper analyzes the asymptotic behavior of a branching-selection particle system by linking it to a censored supercritical Galton-Watson process, providing new insights into its speed dynamics.
Contribution
It introduces a novel connection between a specific branching-selection process and censored Galton-Watson processes to derive asymptotic speed results.
Findings
Asymptotic speed of the particle system determined
Connection established with censored Galton-Watson process
Provides a method to analyze similar branching systems
Abstract
We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by B\'erard and Gou\'er\'e (2010). The proof is based on a connection with a supercritical Galton-Watson process censored at a certain level.
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