Edge-isoperimetric inequalities and influences

Dvir Falik, Alex Samorodnitsky

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)693-712
Number of pages20
JournalCombinatorics Probability and Computing
Volume16
Issue number5
DOIs
StatePublished - Sep 2007
Externally publishedYes

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