Rob Neel (Lehigh University)

Department Colloquium

Speaker: Rob Neel (Lehigh University)

Title: Coupling in geometry and sub-Riemannian diffusions

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 Markov couplings of Riemannian Brownian motions 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 of non-Markovian reflection couplings on sub-Riemannian model spaces by Banerjee-Gordina-Mariano and Bénéfice. 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.