Abstract:
The cutoff phenomenon, introduced by Aldous and Diaconis in the 1980s, describes the abrupt transition to equilibrium in the total variation distance for families of Markov chains models of card shuffling. In this talk, we study the cutoff phenomenon for small stochastic perturbations of dynamical systems, driven by additive or multiplicative noise perturbations. We start our analysis with the celebrated Ornstein-Uhlenbeck process, for which sharp and explicit computations can be carried out, and hence establish precise cutoff results. We then employ techniques from hyperbolic dynamical systems and probabilistic coupling to extend to Langevin dynamics that roughly speaking belongs in the universality class of attraction of the Ornstein-Uhlenbeck process. Furthermore, we study the Cox-Ingersoll-Ross (CIR) process and establish the cutoff phenomenon for its corresponding universality class.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.