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

Jürgen Angst (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: relativistic diffusion; Lorentzian manifolds; poisson boundary; causal boundary

Domaines: Probabilités [math.PR]; Géométrie différentielle [math.DG]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Jürgen Angst. Poisson boundary of a relativistic diffusion in curved space-times: an example. ESAIM: Probability and Statistics, 2015, 19, pp.502-514. ⟨10.1051/ps/2015003⟩. ⟨hal-01044439⟩