Orateur
Description
Time-inhomogeneous Branching Brownian motion (BBM and its discrete counterpart, time-inhomogeneous branching random walks (BRW) may be considered as models for populations undergoing reproduction and dispersion, in an environment that changes slowly over a large time scale T. They have also been studied intensely by physicists and mathematicians as toy models for so-called spin glasses. In this talk, I will first recall classic results (limiting free energy, asymptotics of maximum) which exhibit an interesting explicit dependence on the environment. I will then present recent results. In particular, I will present a study with Alexandre Legrand on a variant of the model with a finite number N of particles, for which we are able to obtain the second-order correction term for its propagation speed. In particular, this correction term exhibits an interesting phase transition when N = exp(T^{1/3}). Based on http://arxiv.org/abs/2402.04917 .
