Edge-isoperimetric inequalities and influences
Combinatorics
2007-05-23 v1
Abstract
We give a combinatorial proof of the result of Kahn, Kalai, and Linial, which states that every balanced boolean function on the -dimensional boolean cube has a variable with influence of at least Omega(\frac{log n}{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 and discuss their possible implications
Cite
@article{arxiv.math/0512636,
title = {Edge-isoperimetric inequalities and influences},
author = {D. Falik and A. Samorodnitsky},
journal= {arXiv preprint arXiv:math/0512636},
year = {2007}
}