WHERE IS THE EXIT POINT

We consider the exit problem for Kramers' model of noise-activated esc ape from a potential well. In this singular perturbation problem the s mall parameter epsilon is the noise strength (temperature measured in units of barrier height). The stochastic dynamics of the escaping traj ectories, conditioned on not returning to a given critical energy cont our, are studied analytically and numerically. The distribution of exi t points on the boundary of the domain of attraction of the stable equ ilibrium point in the phase plane is shown to be spread on the separat rix away from the saddle point. In this problem large deviations theor y fails to predict the distribution of the exit point for finite noise . It is shown, both by a numerical solution of the conditioned dynamic s and analytically, that most of the probability is located at a dista nce O(root epsilon) from the saddle point and vanishes at the saddle p oint. (C) 1998 Elsevier Science B.V. All rights reserved.