A simple reduction from a biased measure on the discrete cube to the uniform measure

Nathan Keller

doi:10.1016/j.ejc.2012.06.003

A simple reduction from a biased measure on the discrete cube to the uniform measure

Nathan Keller

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We show that certain statements related to the Fourier-Walsh expansion of functions with respect to a biased measure on the discrete cube can be deduced from the respective results for the uniform measure by a simple reduction. In particular, we present simple generalizations to the biased measure μ _p of the Bonami-Beckner hypercontractive inequality, and of Talagrand's lower bound on the size of the boundary of subsets of the discrete cube. Our generalizations are tight up to constant factors.

Original language	English
Pages (from-to)	1943-1957
Number of pages	15
Journal	European Journal of Combinatorics
Volume	33
Issue number	8
DOIs	https://doi.org/10.1016/j.ejc.2012.06.003
State	Published - Nov 2012

Bibliographical note

Funding Information:
The author was partially supported by the Adams Fellowship Program of the Israeli Academy of Sciences and Humanities and by the Koshland Center for Basic Research .

Funding

The author was partially supported by the Adams Fellowship Program of the Israeli Academy of Sciences and Humanities and by the Koshland Center for Basic Research .

Funders	Funder number
Koshland Center for Basic Research
Israel Academy of Sciences and Humanities

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10.1016/j.ejc.2012.06.003

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A simple reduction from a biased measure on the discrete cube to the uniform measure

Abstract

Bibliographical note

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