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Statements

Subject Item
dbr:FKG_inequality
rdf:type
yago:WikicatInequalities yago:Quality104723816 yago:Abstraction100002137 yago:Difference104748836 yago:Inequality104752221 yago:Attribute100024264
rdfs:label
Inégalité FKG FKG inequality
rdfs:comment
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. 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).
dct:subject
dbc:Statistical_mechanics dbc:Covariance_and_correlation dbc:Inequalities
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dbp:mr
309498
dbp:first
Jean Cees M. Pieter W. P.C.
dbp:last
Kasteleyn Fortuin Fishburn Ginibre
dbp:pages
89
dbp:title
Correlation inequalities on some partially ordered sets FKG inequality
dbp:url
n17:1103857443
dbp:volume
22
dbp:year
1971
dbo: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. 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).
dbp:author1Link
Cees M. Fortuin
dbp:author2Link
Pieter Kasteleyn
dbp:author3Link
Jean Ginibre
dbp:journal
Communications in Mathematical Physics
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dbr:Inequality
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