- 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.