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On the Holley-Preston inequalities

Published online by Cambridge University Press:  14 November 2011

D. A. Edwards
Affiliation:
Mathematical Institute, Oxford

Synopsis

A new proof of the Holley-Preston generalisation of the Fortuin-Kastelyn-Ginibre inequalities is given, and Batty's extension to the case of infinite products is discussed briefly. An application of the theorems in combinatorial probability theory is described.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1 Batty, C. J. K.. An extension of an inequality of R. Holley. Quart. J. Math. Oxford Ser. 27 (1976), 457462.CrossRefGoogle Scholar
2 Bourbaki, N.. Topologie Générate, Ch. 9, 2nd edn (Paris: Hermann, 1958).Google Scholar
3 Cartier, P.. Inégalites de corrélation en mécanique statistique. Séminaire Bourbaki (25) 431 (1972-1973), 23.Google Scholar
4 Edwards, D. A.. Measures on product spaces and the Holley-Preston inequalities. Bull. London Math. Soc. 8 (1976), 7.Google Scholar
5 Fortuin, C. M., Kastelyn, P. W. and Ginibre, J.. Correlation inequalities on some partially ordered sets. Comm. Math. Phys. 22 (1971), 89103.Google Scholar
6 Holley, R.. Remarks on the FKG inequalities. Comm. Math. Phys. 36 (1974), 227231.CrossRefGoogle Scholar
7 Kleitman, D. J.. Families of non-disjoint subsets. J. Combinatorial Th. 1 (1966), 153155.CrossRefGoogle Scholar
8 Preston, C. J.. A generalization of the FKG inequalities. Comm. Math. Phys. 36 (1974), 233241.CrossRefGoogle Scholar