Threshold for monotone symmetric properties through a logarithmic Sobolev inequality
Probability
2016-08-16 v2
Abstract
Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576--1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017--1054]. The general upper bound for the threshold width of symmetric monotone properties is improved. This follows from a new lower bound on the maximal influence of a variable on a Boolean function. The method of proof is based on a well-known logarithmic Sobolev inequality on . This new bound is shown to be asymptotically optimal.
Keywords
Cite
@article{arxiv.math/0511607,
title = {Threshold for monotone symmetric properties through a logarithmic Sobolev inequality},
author = {Raphaël Rossignol},
journal= {arXiv preprint arXiv:math/0511607},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/009117906000000287 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)