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The FKG Inequality for Partially Ordered Algebras

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  • Siddhartha Sahi

    (Rutgers University)

Abstract

The FKG inequality asserts that for a distributive lattice with log-supermodular probability measure, any two increasing functions are positively correlated. In this paper we extend this result to functions with values in partially ordered algebras, such as algebras of matrices and polynomials.

Suggested Citation

  • Siddhartha Sahi, 2008. "The FKG Inequality for Partially Ordered Algebras," Journal of Theoretical Probability, Springer, vol. 21(2), pages 449-458, June.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:2:d:10.1007_s10959-007-0117-7
    DOI: 10.1007/s10959-007-0117-7
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    References listed on IDEAS

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    1. den Hollander, W.Th.F. & Keane, M., 1986. "Inequalities of FKG type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(1), pages 167-182.
    2. Karlin, Samuel & Rinott, Yosef, 1988. "A generalized Cauchy-Binet formula and applications to total positivity and majorization," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 284-299, October.
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