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arXiv · 2011.06434

Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature

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 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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Martin Kolb, Tobias Weich, Lasse Lennart Wolf. 2020-11-12. Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. https://doi.org/10.1007/s00023-021-01121-5

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