In mathematics, the Fortuin–Kasteleyn–Ginibre (FKG) inequality is a correlation inequality, a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the probabilistic method), due to Cees M. Fortuin, Pieter W. Kasteleyn, and Jean Ginibre (1971). Informally, it says that in many random systems, increasing events are positively correlated, while an increasing and a decreasing event are negatively correlated.
An earlier version, for the special case of i.i.d. variables, called Harris inequality, is due to Theodore Edward Harris (1960), see below. One generalization of the FKG inequality is the Holley inequality (1974) below, and an even further generalization is the Ahlswede–Daykin "four functions" theorem (1978). Furthermore, it has the same conclusion as the Griffiths inequalities, but the hypotheses are different.
Read more about FKG Inequality: The Inequality, Variations On Terminology, A Special Case: The Harris Inequality, Beyond Product Measures, A Generalization: The Holley Inequality, Weakening The Lattice Condition: Monotonicity, See Also
Famous quotes containing the word inequality:
“The doctrine of equality!... But there exists no more poisonous poison: for it seems to be preached by justice itself, while it is the end of justice.... Equality for equals, inequality for unequalsMthat would be the true voice of justice: and, what follows from it, Never make equal what is unequal.”
—Friedrich Nietzsche (18441900)