A Local limit theorem for directed polymers in random media: the continuous and the discrete case.

Vincent Vargas (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this article, we consider two models of directed polymers in random environment: a discrete model and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function is bounded in L^2. Under these assumptions, Sinai proved a local limit theorem for the discrete model, using a perturbation expansion. In this article, we give a new method for proving Sinai's local limit theorem. This new method can be transposed to the continuous setting in which we prove a similar local limit theorem.

Mots clés: Directed polymers in random environment: Local limit theorem

Domaines: Probabilités [math.PR]

Vincent Vargas. A Local limit theorem for directed polymers in random media: the continuous and the discrete case.. 2005. ⟨hal-00004565⟩