# Jerusalem Mathematics Colloquium

Thursday, 1 July 1999, 4:00 pm

Mathematics Bldg., lecture hall 2

##

Professor Zeev Schuss

(Tel-Aviv University)

"Where is the exit point?"

** Abstract: **

The boundary of the domain of attraction of a dynamical system (e.g., a
stable equilibrium, a limit cycle, etc.) is called a separatrix. The exit
problem for a dynamical system driven by noise is to determine the probability
distribution of points on the separatrix where the random trajectories of
the noisy dynamics exit the domain of attraction. This problem is equivalent
to that of finding the Green function for a Dirichlet problem inside the
separatrix. Large Deviations Theory (LDT) predicts that in the limit of
vanishing noise the distribution of the exit points is concentrated at the
absolute minima of the action functional on the separatrix. We show that
in Kramers' classical exit problem for small, but finite noise the exit
points avoid the minimum of the action functional and we determine the
asymptotic form of the exit distribution.

Coffee, Cookies, Company at the faculty lounge at 3:30.

List of talks, 1998-99

List of talks, 1997-98