The influence theorem for product measures on the discrete space {0, 1}N may be extended to probability measures with the property of monotonicity (which is equivalent to "strong positive association"). Corresponding results are valid for probability measures on the cube [0, 1] N that are absolutely continuous with respect to Lebesgue measure. These results lead to a sharp-threshold theorem for measures of random-cluster type, and this may be applied to box crossings in the two-dimensional random-cluster model. © Institute of Mathematical Statistics, 2006.
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Graham, B. T., & Grimmett, G. R. (2006). Influence and sharp-threshold theorems for monotonic measures. Annals of Probability, 34(5), 1726–1745. https://doi.org/10.1214/009117906000000278