an:06270944
Zbl 1292.82026
Ribeiro, Bruno V.; Elskens, Yves
Ornstein-Uhlenbeck limit for the velocity process of an \(N\)-particle system interacting stochastically
EN
J. Stat. Phys. 153, No. 4, 626-640 (2013).
00326340
2013
j
82C22
particle in a heat bath; propagation of chaos; Kac program; stochastic interactions in many dimensions; diffusion on a sphere; Ornstein-Uhlenbeck process; Kac systems
Summary: 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 \(N\to\infty\) limit, a finite number of velocity components are shown to evolve independently and according to an Ornstein-Uhlenbeck process.
Reviewer (Berlin)