Abstract
The kinetic Brownian motion on the sphere bundle of a Riemannian manifold mathbb {M} is a stochastic process that models a random perturbation of the geodesic flow. If mathbb {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.
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