Invariant measure for the process viewed from the particle for 2D random walks in Dirichlet environment

by Adrien Perrel (Université Lyon 1)

Thursday Jun 12, 2025, 2:00 PM → 3:00 PM Europe/Paris

Salle Fokko du Cloux (Université Lyon 1)

Random walks in Dirichlet environment (RWDE) naturally emerge in the study of edge-reinforced random walks. On $\mathbb{Z}^d$, a RWDE is a random walk whose transition probabilities are i.i.d. at each vertex, sampled according to a Dirichlet distribution. In this talk, thanks to a new identity satisfied by the hitting probabilities of the RWDE, we find sufficient conditions for the existence (or non-existence) of an absolutely continuous invariant measure from the point of view of the particle of a RWDE on $\mathbb{Z}^2$.