Influence and sharp-threshold theorems for monotonic measures
Probability
2007-05-23 v1
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.
Cite
@article{arxiv.math/0505057,
title = {Influence and sharp-threshold theorems for monotonic measures},
author = {B. T. Graham and G. R. Grimmett},
journal= {arXiv preprint arXiv:math/0505057},
year = {2007}
}