Shape transition under excess self-intersections for transient random walk

Amine Asselah (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value q(c)(d) = d / d-2. Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.

Domaines: Physique mathématique [math-ph]

Amine Asselah. Shape transition under excess self-intersections for transient random walk. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2010, 46 (1), pp.250--278. ⟨10.1214/09-AIHP318⟩. ⟨hal-00693030⟩