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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 , Pieter W. Kasteleyn, and Jean Ginibre. 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.

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rdf:type	yago:Abstraction100002137 yago:Attribute100024264 yago:Difference104748836 yago:Inequality104752221 yago:Quality104723816 yago:WikicatInequalities
rdfs:label	FKG inequality (en) Inégalité FKG (fr)
rdfs:comment	L’inégalité FKG, notion due à Fortuin, Kasteleyn et Ginibreest une version généralisée de l'inégalité de Tchebychev pour les sommes. C'est une inégalité de corrélation utilisée, par exemple, en théorie de la percolation, et dans l'étude du modèle de graphes aléatoires dû à Paul Erdős et Alfréd Rényi : le (en). (fr) 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 , Pieter W. Kasteleyn, and Jean Ginibre. 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. (en)
dct:subject	Statistical mechanics Covariance and correlation Inequalities
Wikipage page ID	20283423 (xsd:integer)
Wikipage revision ID	1123340233 (xsd:integer)
Link from a Wikipage to another Wikipage	Probabilistic method Percolation theory Statistical mechanics Correlation Covariance and correlation Stochastic ordering Gibbs measure Graph (discrete mathematics) Graph coloring Combinatorics Ahlswede–Daykin inequality Totally ordered Distributive lattice Cylinder (algebra) Expected value Chebyshev's sum inequality Ising model Erdos–Renyi model Ted Harris (mathematician) Coupling (probability) Statistical mechanics Inequalities Hex (board game) Poset Griffiths inequalities I.i.d. Markov chain Honeycomb lattice Phase transitions and critical phenomena Metropolis algorithm Random cluster model Random graph XYZ inequality Hamiltonian cycle Submodular
Link from a Wikipage to an external page	http://www.unige.ch/math/folks/velenik/smbook/index.html http://projecteuclid.org/euclid.cmp/1103857443 http://projecteuclid.org/euclid.cmp/1103859732
sameAs	FKG inequality FKG inequality FKG inequality FKG inequality FKG inequality
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Clarification_needed dbt:Harv dbt:Harvtxt dbt:Short_description dbt:Harvs dbt:Eom
mr	309498 (xsd:integer)
first	Jean (en) P.C. (en) Cees M. (en) Pieter W. (en)
last	Fishburn (en) Fortuin (en) Ginibre (en) Kasteleyn (en)
pages	89 (xsd:integer)
title	Correlation inequalities on some partially ordered sets (en) FKG inequality (en)
url	http://projecteuclid.org/euclid.cmp/1103857443
volume	22 (xsd:integer)
year	1971 (xsd:integer)
has abstract	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 , Pieter W. Kasteleyn, and Jean Ginibre. 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, see . One generalization of the FKG inequality is the 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. (en) L’inégalité FKG, notion due à Fortuin, Kasteleyn et Ginibreest une version généralisée de l'inégalité de Tchebychev pour les sommes. C'est une inégalité de corrélation utilisée, par exemple, en théorie de la percolation, et dans l'étude du modèle de graphes aléatoires dû à Paul Erdős et Alfréd Rényi : le (en). (fr)
author1-link	Cees M. Fortuin (en)
author2-link	Pieter Kasteleyn (en)
author3-link	Jean Ginibre (en)
journal	Communications in Mathematical Physics (en)
gold:hypernym	Inequality
prov:wasDerivedFrom	wikipedia-en:FKG_inequality?oldid=1123340233&ns=0
page length (characters) of wiki page	15747 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:FKG_inequality
is Link from a Wikipage to another Wikipage of	FKG List of inequalities Correlation inequality Ahlswede–Daykin inequality Fortuin Jean Ginibre Pieter Kasteleyn Griffiths inequality Random cluster model

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