Computational and Applied Math Proseminar
joint with Dynamical Systems Seminar

Department of Mathematics, Arizona State University

Tuesday, February 26, 1998, 4:15 PM, GWC 604

Robert S. Maier

Department of Mathematics, University of Arizona,

Large Fluctuations of Randomly Perturbed Dynamical Systems

Abstract A finite-dimensional dynamical system that is subject to random perturbations, such as a white-noise driving force, may fluctuate far from its attractor or attractors. In fact, the random perturbations may induce fluctuations between domains of attraction. Large fluctuations of this sort may be analysed either probabilistically (via the theory of large deviations) or analytically (via WKB-type approximations and matched asymptotic approximations). This talk will explain how very precise asymptotic results may be obtained by the latter technique. In the weak-noise limit of a noise-perturbed system, it turns out that the most probable fluctuational dynamics are described by a variational principle. This permits accurate computation of the frequency with which such fluctuations occur, in appropriate asymptotic regimes. Applications include fluctuation phenomena in statistical physics, chemical physics, and in telecommunications (the overflow of data buffers).

For further information please contact: mittelmann@asu.edu