Influence and sharp-threshold theorems for monotonic measures

Details Influence and sharp-threshold theorems for monotonic measures Influence and sharp-threshold theorems for monotonic measures

2005-05-03

arxiv.org/abs/math/0505057v1

Mathematics

Probability

Scientific paper

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.

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