Curvature Diffusions in General Relativity

Jacques Franchi (1) , Yves Le Jan (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time. We will focus on the case of warped products, especially Robertson-Walker manifolds, and analyse their asymptotic behaviour in the case of Einstein-de Sitter-like manifolds.

Mots clés: Stochastic flow; Robertson-Walker manifolds .; Robertson-Walker manifolds; Covariant relativistic diffusions; General relativity; Lorentz manifold; Riemann curvature tensor

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

Jacques Franchi, Yves Le Jan. Curvature Diffusions in General Relativity. 2010. ⟨hal-00466162⟩