Applications of the FKG Inequality and Its Relatives

R. L. Graham
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R. L. Graham: Bell Laboratories, Department of Discrete Mathematics

A chapter in Mathematical Programming The State of the Art, 1983, pp 115-131 from Springer

Abstract: Abstract In 1971, C. M. Fortuin, P. W. Kasteleyn and J. Ginibre [FKG] published a remarkable inequality relating certain real functions defined on a finite distributive lattice. This inequality, now generally known as the FKG inequality, arose in connection with these authors’ investigations into correlation properties of Ising ferromagnet spin systems and generalized earlier results of Griffiths [Gri] and Harris [Har] (who was studying percolation models). The FKG inequality in turn has stimulated further research in a number of directions, including a variety of interesting generalizations and applications, particularly to statistics, computer science and the theory of partially ordered sets. It turns out that special cases of the FKG inequality can be found in the literature of at least a half dozen different fields, and in some sense can be traced all the way back to work of Chebyshev.

Keywords: Partial Order; Distributive Lattice; Monotonicity Property; Linear Extension; Probability Inequality (search for similar items in EconPapers)
Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-68874-4_6

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DOI: 10.1007/978-3-642-68874-4_6

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