Correlation inequality

Last updated April 15, 2025

A correlation inequality is any of a number of inequalities satisfied by the correlation functions of a model. Such inequalities are of particular use in statistical mechanics and in percolation theory.^[1]

Examples include:

Bell's inequality
FKG inequality
Griffiths inequality, and its generalisation, the Ginibre inequality
Gaussian correlation inequality

References

↑ Ginibre, J. (1972). "Correlation inequalities in statistical mechanics.". Mathematical aspects of statistical mechanics. Providence, R. I.: Amer. Math. Soc. pp. 27–45. MR 0421547.

External links

Fishburn, P. C. (2001) [1994], "Correlation inequalities", Encyclopedia of Mathematics , EMS Press

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[1] Ginibre, J. (1972). "Correlation inequalities in statistical mechanics.". Mathematical aspects of statistical mechanics. Providence, R. I.: Amer. Math. Soc. pp. 27–45. MR 0421547.

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