Quantitative convergence analysis of hypocoercive sampling dynamics

Markov chain Monte Carlo methods based on hypocoercive sampling dynamics provides promising sampling tools for high dimensional probability distributions. In this talk, we will discuss some recent advances on quantitative analysis of convergence of hypocoercive sampling dynamics, including underdamped Langevin dynamics, randomized Hamiltonian Monte Carlo, zigzag process and bouncy particle sampler. The analysis is based on a variational framework for hypocoercivity which combines a Poincare-type inequality in time-augmented state space and an energy estimate. Based on joint works with Yu Cao (NYU) and Lihan Wang (Duke).