For the periodic Lorenz gas Sinai showed that rescaling the trajectory of the tracer particle yields Brownian motion in the limit.  Does there exist a similar result for the random Lorenz gas?  If not, do people believe that there is such a limit?

By the random Lorenz gas I mean: take circular scatterers distributed uniformly at random in the plane conditioned on the scatterers not overlapping.  The scatterers are fixed.  The tracer particle is a point that moves with constant speed and has perfectly elastic collisions with the scatterers.  An initial condition is chosen at random (say, by picking an initial point away from a scatterer and then picking the initial angle uniformly on $[0,2\pi)$.)

The numerical experiments in [Dettmann and Cohen, 2000](http://www.springerlink.com/content/p67k5514w34r1744/) suggest that there is diffusive behaviour for the random Lorenz gas.  This [article by Bunimovich](http://www.bookrags.com/tandf/lorentz-gas-tf/) states that it is believed that velocity autocorrelation decays polynomially, but does not mention whether it decays fast enough for there to be a finite diffusion coefficient.