Limit Theorem for sub-ballistic random walks in Dirichlet environment in dimension $d\ge 3$

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 $\kappa$ for some explicit $\kappa$. We show that the walk, after renormalization, actually converges to a $\kappa$-stable completely asymmetric Levy Process.

66 pages

References in corpus (4)

• Ballistic random walks in random environment at low disorder
• Aging and spin-glass dynamics
• A proof of Sznitman's conjecture about ballistic RWRE
• Sharp ellipticity conditions for ballistic behavior of random walks in random environment