Scaling Limit for the Diffusion Exit Problem

Abstract. In this review, an outline of the so called Freidlin-Wentzell theory and its recent extensions is given. Broadly, this theory studies the exponential rate at which the probabilities of rare events related to random perturbation of ODE decays. The typical situation is when an ODE has several stable equi-libria, in which case, the theory predicts the most likely paths in which the randomly perturbed system goes from one equilibria to another. In recent de-velopments I will outline how recent approaches allows to distinguish between paths that are otherwise exponentially equivalent. An overview of applications of this theory is briefly covered