• Corpus ID: 202572973

# 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}
}
• Published 13 September 2019
• Mathematics
• arXiv: Spectral Theory
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…
1 Citations
Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
• Mathematics
Annales 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

## References

SHOWING 1-10 OF 38 REFERENCES
Kinetic Brownian motion on Riemannian manifolds
• Mathematics
• 2015
We consider in this work a one parameter family of hypoelliptic diffusion processes on the unit tangent bundle $T^1 \mathcal M$ of a Riemannian manifold $(\mathcal M,g)$, collectively called kinetic
Random perturbation to the geodesic equation
We study random “perturbation” to the geodesic equation. The geodesic equation is identified with a canonical differential equation on the orthonormal frame bundle driven by a horizontal vector field
Hypocoercive estimates on foliations and velocity spherical Brownian motion
• Mathematics
• 2016
By further developing the generalized $\Gamma$-calculus for hypoelliptic operators, we prove hypocoercive estimates for a large class of Kolmogorov type operators which are defined on non necessarily
Invariant distributions and time averages for horocycle flows
• Mathematics
• 2003
There are infinitely many obstructions to existence of smooth solutions of the cohomological equation Uu = f , where U is the vector field generating the horocycle flow on the unit tangent bundle SM
Spectral analysis of morse-smale gradient flows.
• Mathematics
• 2016
On a smooth, compact and oriented manifold without boundary, we give a complete description of the correlation function of a Morse-Smale gradient flow satisfying a certain nonresonance assumption.
The hypoelliptic Laplacian and Ray-Singer metrics
• Mathematics
• 2008
This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is
Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces
• Mathematics
International Mathematics Research Notices
• 2019
For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise
Pollicott–Ruelle Resonances for Open Systems
• Mathematics
• 2014
We define Pollicott–Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A
(Non-)Ergodicity of a Degenerate Diffusion Modeling the Fiber Lay Down Process
• Mathematics
SIAM J. Math. Anal.
• 2013
It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic.