Supperdiusion constants for certain nonuniformly hyperbolic systems

CDSNS Colloquium
Monday, October 24, 2016 - 11:06am
1 hour (actually 50 minutes)
Skiles 006
U. Mass Amherst
We investigate deterministic superdiusion in nonuniformly hyperbolic system models in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which differs from the usual requirement that the mean square displacement grow asymptotically linearly in time. We obtain an explicit formula for the superdiffusion constant in terms of the ne structure that originates in the phase transitions as well as the geometry of the configuration domains of the systems. Models that satisfy our main assumptions include chaotic Lorentz gas, Bunimovich stadia, billiards with cusps, and can be apply to other nonuniformly hyperbolic systems with slow correlation decay rates of order O(1/n)