Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces

TL;DR

This paper establishes the spectral convergence of kinetic Brownian motion to the base Laplacian on a broad class of compact locally symmetric spaces, extending previous results on constant curvature surfaces.

Contribution

It generalizes spectral convergence results from constant curvature surfaces to all compact locally symmetric spaces, broadening the understanding of kinetic Brownian motion behavior.

Findings

Spectral convergence proven for kinetic Brownian motion on these spaces

Includes all compact locally symmetric spaces

Extends prior work on constant curvature surfaces

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.