• 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}
}
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
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
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
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
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.
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
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
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
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
TLDR
It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic.
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