H.B. Keller Colloquium

The underdamped Langevin dynamics is perhaps one of the most familiar model used in sampling and non-equilibrium relaxation. Compared with its overdamped limit, the underdamped dynamics exhibits diffusive-to-ballistic acceleration of convergence. Nevertheless, quantifying such acceleration is challenging due to the degeneracy of diffusion. A large literature of hypocoercive estimates has been developed over the years to establish such quantitative rates. 

In this talk, we will discuss some recent progress in sharp convergence rate estimates for underdamped Langevin dynamics, in chi-square divergence and in relative entropy, based on modified L^2 and modified entropy method respectively. Time permitting, we will also discuss application of these estimates to the design and analysis of sampling algorithms.