Poisson boundary of a relativistic diffusion in curved space-times: an example

Abstract

We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with the causal boundary of the underlying manifold.

16 pages, 2 figures

References in corpus (2)

• The causal boundary of product spacetimes
• Lyapunov spectrum of a relativistic stochastic flow in the Poincaré group