Convergence Rate for Langevin Dynamics with Different Potentials

We discuss the long-time convergence behavior of (underdamped) Langevin dynamics, and show how the growth of the potential impacts the convergence rates of the dynamics, via the Poincaré inequality and its weak variants. The analysis is based on the Armstrong-Mourrat variational framework for hypocoercivity which combines a Poincaré-type inequality in time-augmented state space and an L^2 energy estimate. The talk includes my PhD work with Yu Cao (SJTU) and Jianfeng Lu (Duke), as well as my recent work with Giovanni Brigati (IST Austria), Gabriel Stoltz (Ecole des Ponts ParisTech) and Andi Q. Wang (Warwick)