On the stationary measures of anharmonic systems in the presence of a small thermal noise (Q1102640)
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scientific article; zbMATH DE number 4050723
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the stationary measures of anharmonic systems in the presence of a small thermal noise |
scientific article; zbMATH DE number 4050723 |
Statements
On the stationary measures of anharmonic systems in the presence of a small thermal noise (English)
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1986
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We consider certain small stochastic perturbations of a d-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 \(d<3\) then some stability properties of the interaction imply the converse statement; if \(d>2\) then the same is proven for translation invariant measures only. Some methods and results of the author, R. Holley and D. Stroock are extended to second-order systems of stochastic differential equations.
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interacting diffusions
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relative entropy
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singular integrals
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coupled anharmonic oscillators
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Gibbs states
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second-order systems of stochastic differential equations
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