The Reversible Measures of a Conservative System with Finite Range Interactions
We study a system of finite range interacting diffusion processes. The dynamics is described by an infinite dimensional stochastic differential equation. The variables present the amount of charge at various sites of multidimensional lattice ℤ d and the total of charge satisfies a conservation law. We show that each reversible measure of this dynamics is exactly a canonical Gibbs measure corresponding to the given finite range interaction and the converse is also true.
KeywordsRandom Walk Transition Function Stochastic Differential Equation Conservative System Finite Range
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