A Counterexample to a Directed KKL Inequality
Combinatorics
2022-10-06 v1 Computational Complexity
Abstract
We show that the natural directed analogues of the KKL theorem [KKL88] and the Eldan--Gross inequality [EG20] from the analysis of Boolean functions fail to hold. This is in contrast to several other isoperimetric inequalities on the Boolean hypercube (such as the Poincare inequality, Margulis's inequality [Mar74] and Talagrand's inequality [Tal93]) for which directed strengthenings have recently been established.
Cite
@article{arxiv.2210.02035,
title = {A Counterexample to a Directed KKL Inequality},
author = {Quentin Dubroff and Shivam Nadimpalli and Bhargav Narayanan},
journal= {arXiv preprint arXiv:2210.02035},
year = {2022}
}
Comments
5 pages. Comments welcome