EFFECT OF FOCUSING AND CAUSTICS ON EXIT PHENOMENA IN SYSTEMS LACKING DETAILED BALANCE

We study the trajectories followed by a particle weakly perturbed by n oise, when escaping from the domain of attraction of a stable fixed po int. If the particle's stationary distribution lacks detailed balance, a focus may occur along the most probable exit path, leading to a bre akdown of symmetry (if present). The exit trajectory bifurcates, and t he exit location distribution may become ''skewed'' (non-Gaussian). Th e weak-noise asymptotics of the mean escape time are also affected. Ou r methods extend to the study of skewed exit location distributions in stochastic models without symmetry.