Intrinsic area of a self-similar growth-fragmentation

par François Ged

jeudi 6 févr. 2020, 14:30 → 15:30 Europe/Paris

425 (UMPA)

A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. In this talk, we will present a criterion for the existence of an absolutely continuous profile of the tree. When absolutely continuous, we study the asymptotic behaviour of the mass of the ball centered at the root, as the radius decrease to 0.

We will apply these results to the intrinsic volume measure of the Brownian map, exploiting the geometrical connection between growth-fragmentations and random maps recently established by Bertoin et al.