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The N-branching Brownian motion with selection (N-BBM) is a particle system consisting of N independent particles that diffuse as Brownian motions in R, branch at rate one, and whose size is kept constant by removing the leftmost particle at each branching event. We establish the following selection principle: as N the stationary empirical measure of the N-particle system converges to the minimal travelling wave of the associated free boundary PDE. This resolves an open question going back at least to. 19Maillard2012 and GroismanJonckheer, and follows a recent related result by the second author establishing a similar selection principle for the so-called Fleming-Viot particle system Tough23.
Berestycki et al. (Mon,) studied this question.
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