The One Dimensional Stochastic X-Y Model
Consider infinitely many diffusions on an infinite number of circles, one at each integer, that are interacting with each other by means of a finite range potential. We prove that for any finite dimensional marginal of the process, the rate of convergence to the corresponding marginal of the Gibbs state for the potential is exponentially fast.
KeywordsSobolev Inequality GIBBS State Logarithmic Sobolev Inequality Drift Coefficient Finite Difference Operator
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