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Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds

Zhongkai Tao
Dec 2022
摘要
We prove the convergence of the spectrum of the generator of the kineticBrownian motion to the spectrum of the base Laplacian for Riemannian manifolds.This generalizes recent work of Kolb--Weich--Wolf [arXiv:2011.06434] onconstant curvature surfaces and of Ren--Tao [arXiv:2208.13111] on locallysymmetric spaces. As an application, we prove a conjecture of Baudoin--Tardif[arXiv:1604.06813] on the optimal convergence rate to the equilibrium.
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