  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.
