---
_id: '31191'
abstract:
- lang: eng
  text: "The kinetic Brownian motion on the sphere bundle of a Riemannian manifold
    $M$\r\nis a stochastic process that models a random perturbation of the geodesic
    flow.\r\nIf $M$ is a orientable compact constant negatively curved surface, we
    show that\r\nin the limit of infinitely large perturbation the $L^2$-spectrum
    of the\r\ninfinitesimal generator of a time rescaled version of the process converges
    to\r\nthe Laplace spectrum of the base manifold. In addition, we give explicit
    error\r\nestimates for the convergence to equilibrium. The proofs are based on\r\nnoncommutative
    harmonic analysis of $SL_2(\\mathbb{R})$."
author:
- first_name: Martin
  full_name: Kolb, Martin
  last_name: Kolb
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
  full_name: Wolf, Lasse Lennart
  id: '45027'
  last_name: Wolf
citation:
  ama: Kolb M, Weich T, Wolf LL. Spectral Asymptotics for Kinetic Brownian Motion
    on Hyperbolic Surfaces. <i>arXiv:190906183</i>. Published online 2019.
  apa: Kolb, M., Weich, T., &#38; Wolf, L. L. (2019). Spectral Asymptotics for Kinetic
    Brownian Motion on Hyperbolic Surfaces. In <i>arXiv:1909.06183</i>.
  bibtex: '@article{Kolb_Weich_Wolf_2019, title={Spectral Asymptotics for Kinetic
    Brownian Motion on Hyperbolic Surfaces}, journal={arXiv:1909.06183}, author={Kolb,
    Martin and Weich, Tobias and Wolf, Lasse Lennart}, year={2019} }'
  chicago: Kolb, Martin, Tobias Weich, and Lasse Lennart Wolf. “Spectral Asymptotics
    for Kinetic Brownian Motion on Hyperbolic Surfaces.” <i>ArXiv:1909.06183</i>,
    2019.
  ieee: M. Kolb, T. Weich, and L. L. Wolf, “Spectral Asymptotics for Kinetic Brownian
    Motion on Hyperbolic Surfaces,” <i>arXiv:1909.06183</i>. 2019.
  mla: Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic
    Surfaces.” <i>ArXiv:1909.06183</i>, 2019.
  short: M. Kolb, T. Weich, L.L. Wolf, ArXiv:1909.06183 (2019).
date_created: 2022-05-11T10:42:11Z
date_updated: 2022-05-24T13:06:58Z
department:
- _id: '548'
external_id:
  arxiv:
  - '1909.06183'
language:
- iso: eng
publication: arXiv:1909.06183
status: public
title: Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces
type: preprint
user_id: '45027'
year: '2019'
...