Influence and sharp-threshold theorems for monotonic measures

• 成果类型: Article
• 署名作者: Graham, B. T.; Grimmett, G. R.
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000278
• 发表日期: 2006
• 页码: 1726-1745
• 关键词: INEQUALITIES; percolation; SPACES

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.