Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusNoise Stability of Weighted Majority

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: Noise Stability of Weighted Majority [Benjamini et al. (Inst Hautes Études Sci Publ Math 90:5–43, 2001) showed that weighted majority functions of n independent unbiased bits are uniformly stable under noise: when each bit is flipped with probability 𝜖, the probability p𝜖 that the weighted majority changes is at most C𝜖1∕4. They asked what is the best possible exponent that could replace 1∕4. We prove that the answer is 1∕2. The upper bound obtained for p𝜖 is within a factor of π∕2+o(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sqrt {\pi /2}+o(1)$$ \end{document} from the known lower bound when 𝜖 → 0 and n𝜖 →∞.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusNoise Stability of Weighted Majority

Part of the Progress in Probability Book Series (volume 77)
Editors: Vares, Maria Eulália; Fernández, Roberto; Fontes, Luiz Renato; Newman, Charles M.

Loading next page...
 
/lp/springer-journals/in-and-out-of-equilibrium-3-celebrating-vladas-sidoravicius-noise-ZiQmSG3xuW

References (12)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-60753-1
Pages
677 –682
DOI
10.1007/978-3-030-60754-8_27
Publisher site
See Chapter on Publisher Site

Abstract

[Benjamini et al. (Inst Hautes Études Sci Publ Math 90:5–43, 2001) showed that weighted majority functions of n independent unbiased bits are uniformly stable under noise: when each bit is flipped with probability 𝜖, the probability p𝜖 that the weighted majority changes is at most C𝜖1∕4. They asked what is the best possible exponent that could replace 1∕4. We prove that the answer is 1∕2. The upper bound obtained for p𝜖 is within a factor of π∕2+o(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sqrt {\pi /2}+o(1)$$ \end{document} from the known lower bound when 𝜖 → 0 and n𝜖 →∞.]

Published: Nov 4, 2020

Keywords: Noise sensitivity; Boolean functions; Weighted majority; 60C05

There are no references for this article.