Non-extensive condensation in reinforced branching processes

Understand

We study a class of branching processes in which a population consists of immortal individuals equipped with a fitness value.

• Individuals produce offspring with a rate given by their fitness, and offspring may either belong to the same family, sharing the fitness of their parent, or be founders of new families, with a fitness sampled from a fitness distribution.
• Examples that can be embedded in this class are stochastic house-of-cards models, urn models with reinforcement, and the preferential attachment tree of Bianconi and Barabasi.
• Our focus is on the case when the fitness distribution has bounded support and regularly varying tail at the essential supremum.