Influence and sharp-threshold theorems for monotonic measures

被引：34

作者：

Graham, B. T. ^{[1
]}

Grimmett, G. R. ^{[1
]}

机构：

[1] Univ Cambridge, Stat Lab, Cambridge CB3 0WB, England

来源：

ANNALS OF PROBABILITY | 2006年 / 34卷 / 05期

关键词：

influence; sharp threshold; monotonic measure; FKG lattice condition; positive association; random-cluster model; percolation;

D O I：

10.1214/009117906000000278

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The influence theorem for product measures on the discrete space to, {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.

引用

页码：1726 / 1745

页数：20

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