Title:
Ideal gas approximation for a rarefied gas under Kawasaki dynamics.
 (Joint work with Elisabetta Scoppola)
Abstract:
We consider a two-dimensional lattice gas under Kawasaki dynamics.
We show that at fixed temperature in the limit of low  density
the gas particles evolve in a way that is close to an ideal gas, where
particles have
no interaction. In particular, we prove that particle
trajectories are non-superdiffusive and have a diffusive spread-out
property. We also consider the situation where the temperature
and the density tend to zero simultaneously and focus on three
regimes corresponding to the stable, the metastable and the instable gas.
The theorems are formulated in the more general context of systems of
``quasi random walks'', of which we show that the lattice gas under Kawasaki
dynamics is an example. We are able to deal with a large class of initial
conditions having no anomalous concentration of particles and with time horizons that
are much larger than the typical particle collision time.