A Local limit theorem for directed polymers in random media: the continuous and the discrete case
Probability
2015-06-26 v1
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.
Cite
@article{arxiv.math/0503596,
title = {A Local limit theorem for directed polymers in random media: the continuous and the discrete case},
author = {Vincent Vargas},
journal= {arXiv preprint arXiv:math/0503596},
year = {2015}
}