Special Session 172: Stochastic and geometric analysis on manifolds and metric measure spaces

Non-adapted coupling of sub-Riemannian diffusions
Robert Neel
Lehigh University
USA
Co-Author(s):    Liangbing Luo
Abstract:
We 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 recent constructions of non-adapted reflection couplings on sub-Riemannian model spaces by Banerjee-Gordina-Mariano and B\`en\`efice. Moreover, this construction is relatively simple and geometrically appealing, being based on global symmetries of the underlying spaces.