# Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces

@article{Kolb2019SpectralAF, title={Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces}, author={Martin Kolb and Tobias Weich and Lasse Lennart Wolf}, journal={arXiv: Spectral Theory}, year={2019} }

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…

## One Citation

Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature

- MathematicsAnnales Henri Poincaré
- 2021

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

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