On Microscopic Origin of the Fokker - Planck Kinetic Evolution of Hard   Spheres
  The rigorous approach to the description of the kinetic evolution of a many-particle system composed of a trace hard sphere and an environment of finitely many hard spheres is developed. We prove that the evolution of states of a trace hard sphere in an environment can be described within the framework of the marginal distribution function governed by the generalized Fokker -- Planck kinetic equation and an infinite sequence of the explicitly defined functionals of this function. 
I.V. Gapyak, V.I. Gerasimenko
math-ph cond-mat.stat-mech math.AP math.MP