Minimum action paths and rare events in wave equations
Richard Moore
Department of Mathematical Sciences, NJIT,

The importance of rare events has recently been demonstrated in a number of physical systems exhibiting wave behavior, including lasers, optical communication lines, rogue waves in the ocean, and models of turbulence. At the same time, newly developed numerical methods in combination with high-performance parallel computing platforms have made direct numerical simulations of these rare events accessible. We present efficient computational methods to characterize the tails of probability distributions in such complex stochastic systems in the small-noise limit. In particular, we discuss how minimizers of the Freidlin-Wentzell action functional can be used to quantify transition probabilities between stable fixed points of a stochastic dynamical system and to facilitate the computation of expectations related to exit problems.