Diffusion limit for many particles in a periodic stochastic acceleration field - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue The Annals of Applied Probability Année : 2010

Diffusion limit for many particles in a periodic stochastic acceleration field

Résumé

The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener processes. In the limit of vanishing particle mass ${\mathfrak{m}} \to 0$, or equivalently of large noise intensity, we show that the momenta of all $N$ particles converge weakly to $N$ independent Brownian motions, and this convergence holds even if the noise is periodic. This justifies the usual application of the diffusion equation to a family of particles in a unique stochastic force field. The proof rests on the ergodic properties of the relative velocity of two particles in the scaling limit.
Fichier principal
Vignette du fichier
Elskens_Pardoux_Nbody_aap.pdf (262.07 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00336848 , version 1 (05-11-2008)

Identifiants

Citer

Yves Elskens, Etienne Pardoux. Diffusion limit for many particles in a periodic stochastic acceleration field. The Annals of Applied Probability, 2010, 20, pp.2022-2039. ⟨10.1214/09-AAP671⟩. ⟨hal-00336848⟩
106 Consultations
197 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More