Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces

Martin Kolb; Tobias Weich; Lasse Lennart Wolf

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arXiv · 1909.06183

Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces

Martin Kolb·Tobias Weich·Lasse Lennart Wolf

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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 constant negatively 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. In addition, we give explicit error estimates for the convergence to equilibrium. The proofs are based on noncommutative harmonic analysis of $SL_2(\mathbb{R})$.

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BibTeX RIS

Martin Kolb, Tobias Weich, Lasse Lennart Wolf. 2019-09-13. Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces. https://arxiv.org/abs/1909.06183

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