J. Quastel and H.-T. Yau
 Lattice gases, large deviations, and the incompressible
 Navier-Stokes equations
(469K, ps)

ABSTRACT.   We study the incompressible limit for a
 class of stochastic particle systems on the cubic lattice $\ZZ^d,~d=3$.
For initial distributions corresponding to
arbitrary macroscopic $L^2$ initial data the 
distributions of the evolving empirical momentum densities are
shown to have a weak limit supported entirely on global weak solutions of the incompressible Navier-Stokes
equations.  Furthermore explicit exponential rates for the convergence (large deviations)
are obtained. The probability to violate the divergence free condition decays at rate at least
$\exp\{-\e^{-d+1}\}$ while the probability to violate the momentum conservation equation
decays at rate $\exp\{-\e^{-d+2}\}$ with an explicit rate function given by an $H_{-1}$
norm.