Stochastic Stability of Pollicott–Ruelle Resonances

Abstract

Kinetic Brownian motion on the cosphere bundle of a Riemannian manifold $${\mathbb{M}}$$ is a stochastic process that models the geodesic equation perturbed by a random white force of size $${\varepsilon}$$ . When $${\mathbb{M}}$$ is compact and negatively curved, we show that the L 2-spectrum of the infinitesimal generator of this process converges to the Pollicott–Ruelle resonances of $${\mathbb{M}}$$ as $${\varepsilon}$$ goes to 0.