Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds

Abstract

Kinetic Brownian motion is a stochastic process that interpolates between the geodesic flow and Laplacian. It is also an analogue of Bismut’s hypoelliptic Laplacian. We prove the strong convergence of the spectrum of kinetic Brownian motion to the spectrum of base Laplacian for all compact Riemannian manifolds. This generalizes recent work of Kolb--Weich--Wolf on constant curvature surfaces. As an application, we prove the optimal convergence rate of kinetic Brownian motion to equilibrium (given by the spectral gap of base Laplacian) conjectured by Baudoin--Tardif. This is based on joint work with Qiuyu Ren.

Speaker

Tao Zhongkai is a graduate student at UC Berkeley. He's interested in microlocal analysis. His advisor is Maciej Zworski.

https://math.berkeley.edu/~ztao/