Applications of Freidlin-Wentzell theory to population processes 

Freidlin-Wentzell theory grants powerful tools to study the behaviour of dynamical systems perturbed by small noise. It applies naturally to ecological processes modelling large populations, as demographic noise scales as the inverse of the population size. This entails asymptotic estimates for the expected time to extinction, the typical path to extinction and the quasi-stationary distribution conditioned on non-extinction, formulated as large deviations results.