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Mat. Zametki, 2012, Volume 92, Issue 3, Pages 401–409 (Mi mz9856)  

This article is cited in 1 scientific paper (total in 1 paper)

On Decoupling of Functions of Normal Vectors

P. G. Grigor'ev, S. A. Molchanov

University of North Carolina Charlotte, USA

Abstract: Two decoupling type inequalities for functions of Gaussian vectors are proved. In both cases, it turns out that the case of linear functions is the extreme one. The proofs involve certain properties of Wick's (Hermite's) polynomials and a refined version of Schur's theorem on entrywise product of positive definite matrices.

Keywords: decoupling, normally distributed random vector, Wick polynomial, Hermite polynomial, Schur product, Hadamard product, covariance matrix

DOI: https://doi.org/10.4213/mzm9856

Full text: PDF file (450 kB)
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English version:
Mathematical Notes, 2012, 92:3, 362–368

Bibliographic databases:

UDC: 519.213.22
Received: 01.07.2011

Citation: P. G. Grigor'ev, S. A. Molchanov, “On Decoupling of Functions of Normal Vectors”, Mat. Zametki, 92:3 (2012), 401–409; Math. Notes, 92:3 (2012), 362–368

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm9856
  • http://mi.mathnet.ru/eng/mz/v92/i3/p401

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    This publication is cited in the following articles:
    1. P. G. Grigor'ev, S. A. Molchanov, “On Decoupling of Functions of Normal Vectors. II”, Math. Notes, 94:2 (2013), 294–297  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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