Diffusive limit of lattice gas with mixing conditions

We prove, under certain mixing conditions, that the hydrodynamical limit of a stochastic lattice gas on the cubic lattice Z d is governed by a nonlinear diffusion equation. Following [VI], we characterize the diffusion coefficient by a variational formula, which is equivalent to the Green-Kubo formula. The fluctuation-dissipation equation is established rigorously as an important step of the proof. Our mixing conditions are implied by the Dobrushin-Shlosman mixing conditions which are always valid at high temperatures.Mathematic