Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature

The kinetic Brownian motion on the sphere bundle of a Riemannian manifold 𝕄 is a stochastic process that models a random perturbation of the geodesic flow. If 𝕄 is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L^2 -spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold.