Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature

Abstract

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 a 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.

arXiv commentThis is a shortened version of arXiv:1909.06183 but generalized to all constant curvature surfaces instead of negatively curved surfaces

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• Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces