A gradient flow approach to large deviations for diffusion processes

Max Fathi (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such processes. An equivalence between the LDP principle and Gamma-convergence for a sequence of functionals appearing in the gradient flow formulation is proved. As an application, we study large deviations from the hydrodynamic limit for two variants of the Ginzburg-Landau model endowed with Kawasaki dynamics.

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]

Max Fathi. A gradient flow approach to large deviations for diffusion processes. Journal de Mathématiques Pures et Appliquées, 2016, 106 (5), pp.957-993. ⟨10.1016/j.matpur.2016.03.018⟩. ⟨hal-01874821⟩