Pascal Maillard, Toulouse: Branching random walks in heterogeneous environments (Oberseminar Mathematische Stochastik)
Mittwoch, 11.12.2019 17:00 im Raum SRZ 117
Branching random walks are systems of particles which branch and diffuse randomly. They arise in many different contexts such as population models, disordered systems in statistical physics or reaction-diffusion equations. We speak of a heterogeneous environment if the reproduction or the motion of the particles depends on space and/or time on a macroscopic scale. This extra freedom is useful from a modelling perspective, moreover, these models exhibit a much wider range of behaviour than the classical branching random walk. In this talk, I will review their basic properties and present two recent results. The first concerns the efficiency of algorithms for finding low-energy states in Derrida?s continuous random energy model, a Gaussian branching random walk with time-dependent variance. The second concerns the speed of propagation of branching random walks with local selection in heterogenous environment. Based on joint work with (first) Louigi Addario-Berry and (second) Gaël Raoul and Julie Tourniaire.