论文信息 - Events correlated with respect to every subposet of a fixed poset

Events correlated with respect to every subposet of a fixed poset

AbstractPosets $$A,B \subseteq X \times X$$ are said to be (positively) correlated with respect to a third posetR onX (we writeA ↑RB) ifP(A∣R) ≤ P(A∣R ∪ B). HereP(C∣R) is the probability that a randomly chosen linear extension ofR is also a linear extension ofC. We classify posetsR onX such that(x, y) ↑s(u, v) holds for all posetsS onX which are subposets ofR, wherex, y, u, v are distinct elements ofX. On the way to proving this result, we show when a correlation inequality due to Shepp holds strictly.

Graham R. Brightwell

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