Publication: Diffusive limit of lattice gas with mixing conditions
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Date
1997
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International Press of Boston
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Varadhan, 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.
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Abstract
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.
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