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Branching particle systems with selection

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If you have a question about this talk, please contact Elena Yudovina.

Branching processes (either branching random walks or branching Brownian motion) with selection can be seen as a probabilistic genetic model for fixed populations. These families of particles systems, first investigated by Eric Brunet and Bernard Derrida in 1997, consist of a fixed population of N particles, which are given a real-valued fitness. At every branching event, the population size is kept constant through selecting only the N fittest particles.

In this talk, I shall discuss the conjectures of Brunet and Derrida concerning the dynamics of such systems in one dimension, together with the results of two recent rigorous papers on the subject, as well as some of the results and expected results concerning a natural multi-dimensional generalisation of the model.

This talk is part of the Statistical Laboratory Graduate Seminars series.

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