Convergence of gradient flows, large deviations and the Ginzburg-Landau model

In this talk, I will present some results on convergence of sequences of reversible diffusion processes to a deterministic limit, with a particular emphasis on the large deviations. The method is based on the gradient flow formulation of the PDE satisfied by the flow of marginals of the diffusions. As an application, I will discuss the large deviation principle for the Ginzburg-Landau model with random conductances.