Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces

Abstract

We prove the strong convergence of the spectrum of the kinetic Brownian motion to the spectrum of base Laplacian for a large class of compact locally Riemannian homogeneous spaces, in particular all compact locally symmetric spaces. This generalizes recent work of Kolb--Weich--Wolf [arXiv:2011.06434] on constant curvature surfaces.