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Journal Article

On Russo's Approximate Zero-One Law

Michel Talagrand
The Annals of Probability
Vol. 22, No. 3 (Jul., 1994), pp. 1576-1587
Stable URL: http://www.jstor.org/stable/2245033
Page Count: 12

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Topics: Coordinate systems, Integers, Mathematical inequalities, Mathematical functions
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Russo's Approximate Zero-One Law
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Abstract

Consider the product measure μp on {0, 1}n, when 0 $(\operatorname{resp}. 1)$ is given weight $1 - p (\operatorname{resp}. p)$. 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, dμp(A)/dp is large. Thus, in that case, there is a threshold effect and μp(A) jumps from near 0 to near 1 in a small interval.

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