Abstract
We consider certain small stochastic perturbations of ad-dimensional infinite system of coupled anharmonic oscillators. The evolution law is reversible in the Yaglom sense, thus Gibbs states with the given interaction and temperature are stationary measures. If d 2 then the same is proven for translation invariant measures only. The methods and results of Ref. 4, 6–8 are extended to second-order systems of stochastic differential equations.
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