On Russo's Approximate Zero-One Law
Talagrand, Michel
Ann. Probab., Tome 22 (1994) no. 4, p. 1576-1587 / Harvested from Project Euclid
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Consider the product measure $\mu_p$ 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, $d\mu_p(A)/dp$ is large. Thus, in that case, there is a threshold effect and $\mu_p(A)$ jumps from near 0 to near 1 in a small interval.
Publié le : 1994-07-14
Classification:  Approximate zero-one law,  threshold effect,  influence of variables,  28A35,  60K35 
@article{1176988612,
     author = {Talagrand, Michel},
     title = {On Russo's Approximate Zero-One Law},
     journal = {Ann. Probab.},
     volume = {22},
     number = {4},
     year = {1994},
     pages = { 1576-1587},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988612}
}

Talagrand, Michel. On Russo's Approximate Zero-One Law. Ann. Probab., Tome 22 (1994) no. 4, pp.  1576-1587. http://gdmltest.u-ga.fr/item/1176988612/