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Applications of the FKG Inequality and Its Relatives

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Mathematical Programming The State of the Art

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.

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Authors and Affiliations

  1. Department of Discrete Mathematics, Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey, 07974, USA

    R. L. Graham

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  1. R. L. Graham
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  1. Institut für Ökonometrie und Operations Research, Universität Bonn, Nassestraße 2, D-5300, Bonn 1, Germany

    Achim Bachem  & Bernhard Korte  & 

  2. Lehrstuhl für Angewandte Mathematik II, Universität Augsburg, Memminger Straße 6, D-8900, Augsburg, Germany

    Martin Grötschel

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© 1983 Springer-Verlag Berlin Heidelberg

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Graham, R.L. (1983). Applications of the FKG Inequality and Its Relatives. In: Bachem, A., Korte, B., Grötschel, M. (eds) Mathematical Programming The State of the Art. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68874-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-68874-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-68876-8

  • Online ISBN: 978-3-642-68874-4

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