Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature

Angst, J., Bailleul, I., Tardif, C.: Kinetic Brownian motion on Riemannian manifolds. Electron. J. Probab. 20, 1–40 (2015)

Arendt, W., Grabosch, A., Greiner, G., Moustakas, U., Nagel, R., Schlotterbeck, U., Groh, U., Lotz, H.P., Neubrander, F.: One-parameter semigroups of positive operators. Lecture Notes in Mathematics, vol. 1184. Springer, Berlin (1986)

Bismut, J.-M.: The hypoelliptic Laplacian on the cotangent bundle. J. Am. Math. Soc. 18(2), 379–476 (2005)

Bismut, J.-M., Lebeau, G.: The hypoelliptic Laplacian and Ray-Singer metrics. AMS, vol. 167. Princeton University Press, Princeton, NJ (2008)

Baudoin, F., Tardif, C.: Hypocoercive estimates on foliations and velocity spherical Brownian motion. Kinet. Relat. Models 11(1), 1–23 (2018)

Bonthonneau, Y., Weich, T.: Ruelle resonances for manifolds with hyperbolic cusps. J. Eur. Math. Soc. (2021). https://doi.org/10.4171/JEMS/1103

Dyatlov, S., Faure, F., Guillarmou, C.: Power spectrum of the geodesic flow on hyperbolic manifolds. Anal. PDE 8(4), 923–1000 (2015)

Dyatlov, S., Guillarmou, C.: Pollicott–Ruelle resonances for open systems. Ann. Henri Poincaré 17(11), 3089–3146 (2016)

Dang, N.V., Riviere, G.: Spectral analysis of morse-smale gradient flows. Ann. Sci. ENS. 52(6), 1403–1458 (2016)

Drouot, A.: Stochastic stability of Pollicott-Ruelle resonances. Commun. Math. Phys. 356(2), 357–396 (2017)

Dyatlov, S., Zworski, M.: Dynamical zeta functions for Anosov flows via microlocal analysis. Ann. Sci. Éc. Norm. Supér. 49(3), 543–577 (2016)

Engel, K.J., Nagel, R.: One-parameter semigroups for linear evolution equations. Graduate Texts in Mathematics. Springer, New York (2006)

Flaminio, L., Forni, G.: Invariant distributions and time averages for horocycle flows. Duke Math. J. 119(3), 465–526 (2003)

Franchi, J., Le Jan, Y.: Relativistic diffusions and Schwarzschild geometry. Commun. Pure Appl. Math. 60(2), 187–251 (2007)

Faure, F., Sjöstrand, J.: Upper bound on the density of Ruelle resonances for Anosov flows. Commun. Math. Phys. 308(2), 325–364 (2011)

Guillarmou, C., Hilgert, J., Weich, T.: Classical and quantum resonances for hyperbolic surfaces. Math. Ann. 370(3), 1231–1275 (2018)

Guillarmou, C., Hilgert, J., Weich, T.: High frequency limits for invariant Ruelle densities. Ann. Henri Lebesgue 4, 81–119 (2021)

Götz, T., Klar, A., Marheineke, N., Wegener, R.: A stochastic model and associated Fokker-Planck equation for the fiber lay-down process in nonwoven production processes. SIAM J. Appl. Math. 67(6), 1704–1717 (2007)

Grothaus, M., Stilgenbauer, P.: Geometric Langevin equations on submanifolds and applications to the stochastic melt-spinning process of nonwovens and biology. Stoch. Dyn. 13(4), 1350001 (2013)

Grothaus, M., Stilgenbauer, P.: Hypocoercivity for Kolmogorov backward evolution equations and applications. J. Funct. Anal. 267(10), 3515–3556 (2014)

Helffer, B., Nier, F.: Hypoelliptic estimates and spectral theory for Fokker–Planck operators and Witten laplacians. Lecture Notes in Mathematics, vol. 1862. Springer, New York (2005)

Kato, T.: Perturbation theory for linear operators. Grundlehren der mathematischen Wissenschaften, 2 edn. Springer, Berlin (1976)

Kolb, M., Savov, M., Wübker, A.: (Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process. SIAM J. Math. Anal. 45(1), 1–13 (2013)

Küster, B., Weich, T.: Quantum-classical correspondence on associated vector bundles over locally symmetric spaces. Int. Math. Res. Notices 2021(11), 8225–8296 (2019)

Kolb, M., Weich, T., Wolf, L.L.: Spectral asymptotics for kinetic brownian motion on hyperbolic surfaces. arXiv:1909.06183 (2019)

Li, X.-M.: Random perturbation to the geodesic equation. Ann. Probab. 44(1), 544–566 (2016)

Liverani, C.: On contact Anosov flows. Ann. Math. 159(3), 1275–1312 (2004)

Paternain, G.P., Salo, M., Uhlmann, G.: Spectral rigidity and invariant distributions on anosov surfaces. J. Differ. Geom. 98(1), 147–181 (2014)

Reed, M., Simon, B.: Methods of modern mathematical physics II: Fourier analysis, self-adjointness. Academic Press, Methods of modern mathematical physics, New York (1975)

Smith, H.: Parametrix for a semiclassical subelliptic operator. Anal. PDE 13(8), 2375–2398 (2020)

Taylor, M.E.: Noncommutative Harmonic Analysis, Mathematical surveys and monographs, Providence. American Math. Soc, RI (1986)