Rare Events, Action Minimization, and Sharp Interface Limits Draft of proceedings for CRM workshop Singularities in PDE and the Calculus of Variations

Estimating the probability of and mechanism for rare events is a physically relevant and mathematically interesting question. Focussing on issues related to “constrained switching events,” we describe differences from the classical Arrhenius picture and how action minimization can be used as a tool. As a specific example, we turn to the stochastic Allen-Cahn equation and explain recent results for the scaling of the action problem and the sharp interface limit.