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. It was obtained by studying the random cluster model.
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.
In mathematics, the Fortuin–Kasteleyn–Ginibre (FKG) inequality is a correlation inequality, a fundamental tool in statistical mechanics and probabilistic...
FKG may refer to: Falkirk Grahamston railway station, in Scotland FKGinequality Furkating Junction railway station, in Assam, India Genk railway station...
_{z}\sigma _{y}\rangle .} This inequality can be used to establish the sharpness of phase transition for the Ising model. This inequality is proven first for a...
The proof uses the Ahlswede–Daykin inequality. FKGinequality Fishburn, Peter C. (1984), "A correlational inequality for linear extensions of a poset"...
functions on Γ. This yields Chebyshev's sum inequality. For extension to partially ordered sets, see FKGinequality. The thermodynamic limit of the correlations...
matrix theory (see circular law), statistical mechanics (see FKGinequality, Ginibre inequality), and partial differential equations. With Martine Le Berre...
sometimes referred to as FK models. In 1971 they used it to obtain the FKGinequality. Post 1987, interest in the model and applications in statistical physics...
Fortuin [Wikidata] (born 1940 ), Dutch mathematician; the "F" in the FKGinequality and the FK cluster model Clyde Fortuin (born 1995), South African cricketer...
with C. M. Fortuin he developed random cluster model and obtained the FKGinequality. For Bernoulli percolation on graphs he formulated the Bunkbed conjecture...
statistical mechanics known for the Fortuin-Kasteleyn-Ginibre inequality (FKGinequality); in Leiden (d.1996) Died: Anatole France (pen name for Jacques-Anatole...
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