Reinforced Galton--Watson processes III: Empirical offspring distributions

Abstract

Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution depends on the empirical offspring distribution of each individual along its ancestral lineage. We are interested here in asymptotic properties of the empirical distributions observed in the population, such as concentration, evanescence and persistence. For this, we incorporate tools from the theory of large deviations to our preceding analysis [arXiv:2306.02476,arXiv:2310.19030].