Noise stability is computable and approximately low-dimensional
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1701.01483.pdf
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Author(s)
De, Anindya
Mossel, Elchanan
Neeman, Joe
Date Issued
2017
Journal
Leibniz International Proceedings in Informatics
Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Citation
De, Anindya, et al. Noise Stability Is Computable and Approximately Low-Dimensional. Edited by Marc Herbstritt, 2017. © Anindya De, Elchanan Mossel, and Joe Neeman.
Version
Author's final manuscript
Abstract
Questions of noise stability play an important role in hardness of approximation in computer science as well as in the theory of voting. In many applications, the goal is to find an optimizer of noise stability among all possible partitions of R[superscript n] for n ≥ 1 to k parts with given Gaussian measures μ[superscript 1], . . . , μ[superscript k]. We call a partition ϵ-optimal, if its noise stability is optimal up to an additive ϵ. In this paper, we give an explicit, computable function n(ϵ) such that an ϵ-optimal partition exists in R[superscript n(ϵ)]. This result has implications for the computability of certain problems in non-interactive simulation, which are addressed in a subsequent work. Keywords: Gaussian noise stability; Plurality is stablest; Ornstein Uhlenbeck operator
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.4230/LIPIcs.CCC.2017.10
