Correlation inequalities and a conjecture for permanents

Abstract

This paper presents conditions on nonnegative real valued functionsf 1,f 2,...,f m andg 1,g 2,...g m implying an inequality of the type

$$\mathop \Pi \limits_{i = 1}^m \int {f_i (x)d\mu } (x) \leqslant \mathop \Pi \limits_{i = 1}^m \int {g_i (x)d\mu } (x).$$

This “2m-function” theorem generalizes the “4-function” theorem of [2], which in turn generalizes a “2-function” theorem ([8]) and the celebrated FKG inequality. It also contains (and was partly inspired by) an “m against 2” inequality that was deduced in [5] from a general product theorem.

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This work was supported in part by NSF grant DMS-9001274.

This work was supported in part by NSF grant DMS87-03541 and CCR89-11388.

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Rinott, Y., Saks, M. Correlation inequalities and a conjecture for permanents. Combinatorica 13, 269–277 (1993). https://doi.org/10.1007/BF01202353

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AMS subject classification code (1991)

  • 60 C 05
  • 60 E 15
  • 06 D 99
  • 05 D 99
  • 06 A 07