93-156 Robert S.Maier and Daniel L.Stein University of Arizona

The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance (672K, PostScript, 11 pages) Jun 1, 93

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Abstract. We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a _focus_ may occur along the most probable exit path, leading to a breakdown of symmetry (if present). The exit trajectory bifurcates, and the exit location distribution may become `skewed' (non-Gaussian). The weak-noise asymptotics of the mean escape time are strongly affected. Our methods extend to the study of skewed exit location distributions in stochastic models without symmetry.

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