Navier-Stokes equations for stochastic particle systems on the lattice

We introduce a class of stochastic models of particles on the cubic lattice ℤ d with velocities and study the hydrodynamical limit on the diffusive spacetime scale. Assuming special initial conditions corresponding to the incompressible regime, we prove that in dimensiond≧3 there is a law of large numbers for the empirical density and the rescaled empirical velocity field. Moreover the limit fields satisfy the corresponding incompressible Navier-Stokes equations, with viscosity matrices characterized by a variational formula, formally equivalent to the Green-Kubo formula.