A correlation inequality is any of a number of inequalities satisfied by the
correlation function
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables re ...
s of a model. Such inequalities are of particular use in
statistical mechanics and in
percolation theory
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnecte ...
.
Examples include:
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Bell's inequality
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FKG inequality
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Griffiths inequality, and its generalisation, the
Ginibre inequality
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Gaussian correlation inequality
The Gaussian correlation inequality (GCI), formerly known as the Gaussian correlation conjecture (GCC), is a mathematical theorem in the fields of mathematical statistics and convex geometry. The statement
The Gaussian correlation inequality stat ...
References
External links
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Probabilistic inequalities
Statistical mechanics
Inequalities
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