Ornstein-Uhlenbeck limit for the velocity process of an $N$-particle system interacting stochastically

Bruno Vieira Ribeiro; Yves Elskens

Ornstein-Uhlenbeck limit for the velocity process of an $N$-particle system interacting stochastically

Mathematical Physics 2013-08-16 v2 Statistical Mechanics math.MP Chaotic Dynamics

Authors: Bruno Vieira Ribeiro , Yves Elskens

Abstract

An $N$ -particle system with stochastic interactions is considered. Interactions are driven by a Brownian noise term and total energy conservation is imposed. The evolution of the system, in velocity space, is a diffusion on a $(3N-1)$ -dimensional sphere with radius fixed by the total energy. In the $N\rightarrow\infty$ limit, a finite number of velocity components are shown to evolve independently and according to an Ornstein-Uhlenbeck process.

Keywords

n-particle system stochastic interactions brownian noise energy conservation diffusion on sphere ornstein-uhlenbeck process large n limit

Cite

@article{arxiv.1304.4034,
  title  = {Ornstein-Uhlenbeck limit for the velocity process of an $N$-particle system interacting stochastically},
  author = {Bruno Vieira Ribeiro and Yves Elskens},
  journal= {arXiv preprint arXiv:1304.4034},
  year   = {2013}
}

Comments

19 pages ; streamlined notations ; new section on many particles with momentum conservation ; new appendix on Kac system

Ornstein-Uhlenbeck limit for the velocity process of an $N$-particle system interacting stochastically

Abstract

Keywords

Cite

Comments

Related papers