Non-extensive condensation in reinforced branching processes

Cécile Mailler (University of Bath)

Frank Adams 2,

In this joint work with Steffen Dereich and Peter Mörters, we introduce and study a branching process with both a reinforcement and a mutation dynamics. Our model incompasses as a particular case the Bianconi and Barab\'asi's preferential attachment graph with fitnesses but also a selection and mutation population branching process. We prove that this model exhibits, under some conditions on the parameters, a condensation phenomenon, and more precisely that ``the winner does not take it all'', disproving a claim made in the physics literature about the Bianconi and Barab\'asi's model.

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