Summary
An infinite lattice system of interacting diffusion processes is characterized as a Gibbs distribution on\(C[0,1]^{Z^d }\) with continuous local conditional probabilities. Using estimates for the Vasserstein metric onC[0, 1], Dobrushin's contraction technique is applied in order to obtain information about macroscopic properties of the entire diffusion process.
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Deuschel, J.D. Infinite-dimensional diffusion processes as gibbs measures on\(C[0,1]^{Z^d }\) . Probab. Th. Rel. Fields 76, 325–340 (1987). https://doi.org/10.1007/BF01297489
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DOI: https://doi.org/10.1007/BF01297489