{"department":[{"_id":"548"}],"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 $SL_2(\\mathbb{R})$."}],"publication":"arXiv:1909.06183","title":"Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces","author":[{"first_name":"Martin","full_name":"Kolb, Martin","last_name":"Kolb"},{"first_name":"Tobias","last_name":"Weich","id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919"},{"first_name":"Lasse Lennart","last_name":"Wolf","full_name":"Wolf, Lasse Lennart","id":"45027"}],"citation":{"mla":"Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces.” <i>ArXiv:1909.06183</i>, 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>.","short":"M. Kolb, T. Weich, L.L. Wolf, ArXiv:1909.06183 (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.","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} }","ama":"Kolb M, Weich T, Wolf LL. Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces. <i>arXiv:190906183</i>. Published online 2019."},"status":"public","_id":"31191","user_id":"45027","language":[{"iso":"eng"}],"date_created":"2022-05-11T10:42:11Z","external_id":{"arxiv":["1909.06183"]},"type":"preprint","year":"2019","date_updated":"2022-05-24T13:06:58Z"}