Abstract
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.
Citation
B. T. Graham. G. R. Grimmett. "Influence and sharp-threshold theorems for monotonic measures." Ann. Probab. 34 (5) 1726 - 1745, September 2006. https://doi.org/10.1214/009117906000000278
Information