Pollicott-Ruelle resonances via kinetic Brownian motion

Abstract

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 $\epsilon \to 0$.

38 pages. The first and second versions deal with the case of surfaces and are technically simpler than the third version

Cited by in corpus (2)

• Mathematical Study of Scattering Resonances
• On the Pollicott-Ruelle resonances