Rs. Maier et Dl. Stein, EFFECT OF FOCUSING AND CAUSTICS ON EXIT PHENOMENA IN SYSTEMS LACKING DETAILED BALANCE, Physical review letters, 71(12), 1993, pp. 1783-1786
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.