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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00004565
Contributor : Vincent Vargas <>
Submitted on : Friday, March 25, 2005 - 1:42:09 PM
Last modification on : Tuesday, May 14, 2019 - 11:02:13 AM
Long-term archiving on : Thursday, April 1, 2010 - 9:07:28 PM

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

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