Distribution and localization of large local times of the random walk in random environment on a Bienaymé-GW tree

par Loïc de Raphélis

jeudi 14 déc. 2023, 14:00 → 15:00 Europe/Paris

We consider the nearest-neighbor random walk on a Bienaymé-Galton-Watson tree in random environment. Under certain conditions on the law of the environment, the random walk is subdiffusive. In this case, we are interested in the distribution of the local times of the walk, as well as their localization in the tree. We will show that when taking a large number of excursions from the root, these local times correctly normalized converge towards a decorated Poisson process of which we will give a precise description. We will also show that they localize either close to the root, or according to the Gibbs measure induced by the environment on the boundary of the tree.
 

This talk is based on a joint work with Xinxin Chen.