Lower bound on the correlation between monotone families in the average case
type: Item
instance of: scholarly article
title: Lower bound on the correlation between monotone families in the average case
zbMATH Open document ID: 1171.42022
author: Nathan Keller
published in: Advances in Applied Mathematics
publication date: 2009-06-11T00:00:00Z
review text: Correlation inequalities between monotone functions play an important role in numerous areas, including probability, combinatorics etc. This paper considers monotone functions on the discrete cube \(\{0,1\}^n\) endowed with the uniform measure, and especially Boolean functions that can be treated as characteristic functions of subsets of the discrete cube. It is shown that when the correlation is averaged over all pairs \(A,B \in T\), for any family \(T\) of monotone subsets of \(\{0,1\}^n\), the lower bound asserted in [\textit{M. Talagrand}, Combinatorica 16, No. 2, 243--258 (1996; Zbl 0861.05008)] can be improved and more precise estimates on the average correlation can be given.
Mathematics Subject Classification ID: 42C99
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 5564307
zbMATH Keywords: correlation inequalities
zbMATH Keywords: influences
zbMATH Keywords: discrete Fourier analysis
reviewed by: Pedro A. Morettin
MaRDI profile type: Publication
full work available at URL: j.aam.2008.11.004
OpenAlex ID: W2051397982
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DOI: 10.1016/J.AAM.2008.11.004
description: scientific article; zbMATH DE number 5564307