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 in asymptotic properties of the latter, such as concentration, evanescence and persistence.
In addition to earlier results about the mean behavior of reinforced Galton--Watson processes, tools from the theory of large deviations play an important part in the study.
Based on an ongoing work with Bastien Mallein (Toulouse)