| 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. (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) |
| dbo:wikiPageExternalLink |
http://www.unige.ch/math/folks/velenik/smbook/index.html http://projecteuclid.org/euclid.cmp/1103857443 http://projecteuclid.org/euclid.cmp/1103859732 |
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| dbp:author1Link |
Cees M. Fortuin (en) |
| dbp:author2Link |
Pieter Kasteleyn (en) |
| dbp:author3Link |
Jean Ginibre (en) |
| dbp:first |
Jean (en) P.C. (en) Cees M. (en) Pieter W. (en) |
| dbp:journal |
Communications in Mathematical Physics (en) |
| dbp:last |
Fishburn (en) Fortuin (en) Ginibre (en) Kasteleyn (en) |
| dbp:mr |
309498 (xsd:integer) |
| dbp:pages |
89 (xsd:integer) |
| dbp:title |
Correlation inequalities on some partially ordered sets (en) FKG inequality (en) |
| dbp:url |
http://projecteuclid.org/euclid.cmp/1103857443 |
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22 (xsd:integer) |
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1971 (xsd:integer) |
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dbc:Statistical_mechanics dbc:Covariance_and_correlation dbc:Inequalities |
| gold:hypernym |
dbr:Inequality |
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yago:Abstraction100002137 yago:Attribute100024264 yago:Difference104748836 yago:Inequality104752221 yago:Quality104723816 yago:WikicatInequalities |
| 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) |
| rdfs:label |
FKG inequality (en) Inégalité FKG (fr) |
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