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Branching Brownian motion with selection

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Consider supercritical branching Brownian motion on the real line (particles diffuse according to Brownian motions and reproduce at constant rate), where additionally a particle gets killed whenever N particles are to the right of it (we call this model the N-BBM). Brunet, Derrida, Mueller and Munier predicted detailed statistics of the fluctuations of this model in the large population limit. In this talk, I will present a related model, which consists of introducing a random space-time barrier at which particles are instantaneously killed in such a way that the population size stays almost constant over time. I will show how one can prove the physicists predictions for this approximate model, which is a first step in the study of the N-BBM.

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