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

2014/05/01 by Jürgen Angst, Angst, Jürgen
Mathematics · Physics and Astronomy · #60J45 #60J60 #83F05 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.DG #math.MP #math.PR #msc:60J45 #msc:60J60 #msc:83F05

paper · pdf · doi:10.48550/arxiv.1405.0148

16 pages, 2 figures

arxiv created 2014/05/01 · arxiv updated 2014/05/02

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.

Related

• On the Poisson boundary of the relativistic Brownian motion
• Asymptotic behavior of a relativistic diffusion in Robertson-Walker space-times
• Dévissage of a Poisson boundary under equivariance and regularity conditions
• A pathwise approach to relativistic diffusions
• Relativistic diffusion of particles with a continuous mass spectrum