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.

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

References in corpus (1)

• Power spectrum of the geodesic flow on hyperbolic manifolds