On Russo's Approximate Zero-One Law
On Russo's Approximate Zero-One Law
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论罗素近似零一定律
DOI：
10.1214/aop/1176988612
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发表时间：
1994
影响因子：
2.3
通讯作者：
M. Talagrand
中科院分区：
文献类型：
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作者：
M. Talagrand
考虑{0，1} n上的乘积测度μ p，当0（分别为1)被赋予权重1-p（分别p）。考虑{0，1} n的单调子集A。我们对以下陈述给出了精确的定量形式：如果A不太依赖于任何给定的坐标，则dμ p（A）/dp很大。因此，在这种情况下，存在阈值效应并且μ p（A）在小的间隔内从接近0跳到接近1
Consider the product measure μ p on {0, 1} n , when 0 (resp. 1) is given weight 1-p (resp. p). Consider a monotone subset A of {0, 1} n . We give a precise quantitative form to the following statement: if A does not depend much on any given coordinate, dμ p (A)/dp is large. Thus, in that case, there is a threshold effect and μ p (A) jumps from near 0 to near 1 in a small interval