Correlation inequality - AbsoluteAstronomy.com

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

and statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, a correlation inequality is one of a number of inequalities satisfied by the correlation function

Correlation function

A correlation function is the correlation between random variables at two different points in space or time, usually as a function of the spatial or temporal distance between the points...

s of a model. Such inequalities are of particular use in statistical mechanics

Statistical mechanics

Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...

and in percolation theory

Percolation theory

In mathematics, percolation theory describes the behavior of connected clusters in a random graph. The applications of percolation theory to materials science and other domains are discussed in the article percolation.-Introduction:...

.

Examples include:

Bell's inequality
FKG inequality
FKG inequality
The FKG inequality is a correlation inequality, a fundamental tool in statistical mechanics and probabilistic combinatorics , due to...
Griffiths inequality
Griffiths inequality
In statistical mechanics, the Griffiths inequality , named after Robert B. Griffiths, is a correlation inequality for ferromagnetic spin systems...
Ginibre inequality

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