A Counterexample to the "Majority is Least Stable" Conjecture
Computational Complexity
2017-03-27 v2 Probability
Abstract
We exhibit a linear threshold function in 5 variables with strictly smaller noise stability (for small values of the correlation parameter) than the majority function on 5 variables, thereby providing a counterexample to the "Majority is Least Stable" Conjecture of Benjamini, Kalai, and Schramm.
Keywords
Cite
@article{arxiv.1703.07657,
title = {A Counterexample to the "Majority is Least Stable" Conjecture},
author = {Vishesh Jain},
journal= {arXiv preprint arXiv:1703.07657},
year = {2017}
}
Comments
After this note appeared on the arXiv, we were informed that Sivakanth Gopi (in 2013), and Steven Heilman and Daniel Kane (in 2017), already independently observed that the "Majority is Least Stable" conjecture, as stated, is not true