Noise Stability of Weighted Majority

dc.creatorPeres, Yuval
dc.date2004-12-19
dc.date.accessioned2026-07-07T05:15:27Z
dc.date.available2026-07-07T05:15:27Z
dc.descriptionBenjamini, Kalai and Schramm (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 $p_ε$ that the weighted majority changes is at most $Cε^{1/4}$. 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 $p_ε$ is within a factor of $\sqrt{π/2}+o(1)$ from the known lower bound when $ε\to 0$ and $nε\to \infty$.
dc.descriptionsix pages
dc.identifierhttps://arxiv.org/abs/math/0412377
dc.identifierhttp://arxiv.org/abs/math/0412377
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73633
dc.subjectProbability
dc.subjectCombinatorics
dc.subject60C05
dc.titleNoise Stability of Weighted Majority
dc.typetext

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