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arxiv: 1703.07657 · v2 · pith:6BPHBJZRnew · submitted 2017-03-22 · 💻 cs.CC · math.PR

A Counterexample to the "Majority is Least Stable" Conjecture

Vishesh Jain This is my paper
classification 💻 cs.CC math.PR
keywords majorityconjecturecounterexamplefunctionleaststablevariablesbenjamini
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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.

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    Nearly tight bounds characterize the noise regimes where the Majority is Least Stable and Non-Interactive Correlation Distillation conjectures hold for Boolean functions of dimension n≥5, with full validity for n=3, p...