Pollicott-Ruelle resonances via kinetic Brownian motion

The 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 $\epsilon$. When $\mathbb{M}$ is compact with negative curvature we show that the $L^2$-spectrum of the infinitesimal generator of this process converges to the Pollicott–Ruelle resonances of $\mathbb{M}$ as $\epsilon \to 0$.