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 $\epsilon \to 0$.

arXiv comment38 pages. The first and second versions deal with the case of surfaces and are technically simpler than the third version

References in corpus (2)

• Ruelle zeta function at zero for surfaces
• Scattering resonances for highly oscillatory potentials

Cited by in corpus (6)

• Resonances for random highly oscillatory potentials
• Viscosity limits for 0th order pseudodifferential operators
• Mathematical Study of Scattering Resonances
• Resonances and viscosity limit for the Wigner-von Neumann type Hamiltonian
• Vlasov-Fokker-Planck equation: stochastic stability of resonances and unstable manifold expansion
• On the Pollicott-Ruelle resonances