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Annealed upper tails for the energy of a charged polymer

Amine Asselah — 2011

Annales de l'I.H.P. Probabilités et statistiques

We study the upper tails for the energy of a randomly charged symmetric and transient random walk. We assume that only charges on the same site interact pairwise. We consider estimates, that is when we average over both randomness, in dimension three or more. We obtain a large deviation principle, and an explicit rate function for a large class of charge distributions.

Shape transition under excess self-intersections for transient random walk

Amine Asselah — 2010

Annales de l'I.H.P. Probabilités et statistiques

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

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