, Volume 13, Issue 3, pp 269-277

Correlation inequalities and a conjecture for permanents

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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.