Abstract
In this paper we derive tight bounds on the expected value of products of low influence functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated probability spaces, on a generalization of an invariance principle recently obtained with O’Donnell and Oleszkiewicz for multilinear polynomials with low influences and bounded degree and on properties of multi-dimensional Gaussian distributions.
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Supported by a Sloan fellowship in Mathematics, by BSF grant 2004105, NSF Career Award (DMS 054829) and by ONR award N00014-07-1-0506. Part of this work was carried out while the author was visiting IPAM, UCLA
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Mossel, E. Gaussian Bounds for Noise Correlation of Functions. Geom. Funct. Anal. 19, 1713–1756 (2010). https://doi.org/10.1007/s00039-010-0047-x
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DOI: https://doi.org/10.1007/s00039-010-0047-x
Keywords and phrases
- Invariance
- discrete harmonic analysis
- voting
- hardness of approximation
- Gaussian isoperimetric inequalities