A mechanical model of Brownian motion

We consider a dynamical system consisting of one large massive particle and an infinite number of light point particles. We prove that the motion of the massive particle is, in a suitable limit, described by the Ornstein-Uhlenbeck process. This extends to three dimensions previous results by Holley in one dimension.On leave of the Institut für Theoretische Physik I der Universität Münster. Supported by a Nato fellowshipSupported by NSF Grant, No. PHY 78-03816Supported by NSF Grant, Phy 78-15920