Shepp, Larry A2023-05-232023-05-2319822016-08-03https://repository.upenn.edu/handle/20.500.14332/47708Consider random variables x1,⋯,xn, independently and uniformly distributed on the unit interval. Suppose we are given partial information, Γ, about the unknown ordering of the x's; e.g., Γ = {x1 < x12, x7 < x5,⋯}. We prove the "XYZ conjecture" (originally due to Ivan Rival, Bill Sands, and extended by Peter Winkler, R. L. Graham, and other participants of the Symposium on Ordered Sets at Banff, 1981) that P(x1FKG inequalityXYZ conjecturepartially ordered setsProbabilityArticle