Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature

<jats:title>Abstract</jats:title><jats:p>The kinetic Brownian motion on the sphere bundle of a Riemannian manifold <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {M}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> is a stochastic process that models a random perturbation of the geodesic flow. If <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {M}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold.</jats:p>