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Shape transition under excess self-intersections for transient random walk

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

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