Geometric couplings and sub-Riemannian diffusions
Rob Neel, Lehigh University
Abstract: We recall the notion of a coupling of two stochastic processes and its application to showing convergence to equilibrium. We then describe the classical applications to Riemannian geometry, and how these natural constructions fail in sub-Riemannian geometry, even for the simplest case of the Heisenberg group. After reviewing the situation, we describe an improvement and extension of constructions by Banerjee-Gordina-Mariano and Bénéfice of non-Markovian reflection couplings on sub-Riemannian model spaces. Moreover, this construction is relatively simple and geometrically appealing, being based on global symmetries of the underlying spaces. This talk is based on joint work with Liangbing Luo.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
