Inequalities of FKG type

✍ Scribed by W.Th.F. den Hollander; M. Keane

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 922 KB
• Volume: 138
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(86)90178-0

✦ Synopsis

In 1971 Fortuin, Kasteleyn and Ginibre proved a correlation inequality for monotone functions on certain partially ordered sets. This inequality has become a standard tool in the rigorous analysis of diverse stochastic models, such as those arising in percolation theory, statistical mechanics of spin systems and combinatorics. Several generalizations of the FKG inequality have appeared in the literature, notably by Holley in 1974 and by Ahlswede-Daykin in 1978. We review the three inequalities, present simplified proofs and list a few major applications. We also prove chains of "intermediate" inequalities stronger than the FKG and Holley inequalities, which may be useful for understanding and for future development.