Varadhan, S. R. S.Yau, Horng-Tzer2018-03-061997Varadhan, S. R. S., and Horng-Tzer Yau. 1997. “Diffusive Limit of Lattice Gas with Mixing Conditions.” Asian Journal of Mathematics 1 (4): 623–678. doi:10.4310/ajm.1997.v1.n4.a1.1093-6106http://nrs.harvard.edu/urn-3:HUL.InstRepos:34900024We 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.en-USJournal Article2018-03-0610.4310/AJM.1997.v1.n4.a1