Abstract:
The joint diffusion of two particles in a dynamical environment was shown
to become asymptotically independent for a 1-D degenerate mechanical model
(Harris-Spitzer model) by the speaker in 1980, and for stochastic models
of symmetric exclusion by Kipnis and Varadhan in 1985. In truly mechanical
systems, however, where the interaction of the particles also involves
energy exchange, this independence does not hold anymore. The phenomenon
is explained and demonstrated for a stochastic model of two Lorentz disks.
The diffusive limit of the motion of one particle is a mixture of Wiener
processes and the random covariances are determined by the Boltzmann's
Stosszahlansatz. The results are joint with Zs. Pajor-Gyulai.