Limit theorem for sub-ballistic Random Walks in Dirichlet Environment in dimension d≥3

Abstract

We look at random walks in Dirichlet environment. It was known that in dimension $d\ge 3$, if the walk is sub-ballistic, the displacement of the walk is polynomial of order κ for some explicit κ. We show that the walk, after renormalization, actually converges to a κ-stable completely asymmetric Lévy Process.