Edge-isoperimetric inequalities and influences

Dvir Falik; Alex Samorodnitsky

doi:10.1017/S0963548306008340

Edge-isoperimetric inequalities and influences

Dvir Falik^*, Alex Samorodnitsky

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

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

24 Scopus citations

Abstract

We give a combinatorial proof of the result of Kahn, Kalai and Linial [16], which states that every balanced boolean function on the n-dimensional boolean cube has a variable with influence of at least Ω(logn/n) The methods of the proof are then used to recover additional isoperimetric results for the cube, with improved constants. We also state some conjectures about optimal constants.

Original language	American English
Pages (from-to)	693-712
Number of pages	20
Journal	Combinatorics Probability and Computing
Volume	16
Issue number	5
DOIs	https://doi.org/10.1017/S0963548306008340
State	Published - Sep 2007

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title = "Edge-isoperimetric inequalities and influences",

abstract = "We give a combinatorial proof of the result of Kahn, Kalai and Linial [16], which states that every balanced boolean function on the n-dimensional boolean cube has a variable with influence of at least Ω(logn/n) The methods of the proof are then used to recover additional isoperimetric results for the cube, with improved constants. We also state some conjectures about optimal constants.",

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AB - We give a combinatorial proof of the result of Kahn, Kalai and Linial [16], which states that every balanced boolean function on the n-dimensional boolean cube has a variable with influence of at least Ω(logn/n) The methods of the proof are then used to recover additional isoperimetric results for the cube, with improved constants. We also state some conjectures about optimal constants.

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Edge-isoperimetric inequalities and influences

Abstract

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