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On decoupling of functions of normal vectors

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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 ofWick’s (Hermite’s) polynomials and a refined version of Schur’s theorem on entrywise product of positive definite matrices.

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Authors and Affiliations

  1. University of North Carolina, Charlotte, USA

    P. G. Grigoriev & S. A. Molchanov

Authors
  1. P. G. Grigoriev
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  2. S. A. Molchanov
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Corresponding author

Correspondence to P. G. Grigoriev.

Additional information

Published in Russian in Matematicheskie Zametki, 2012, Vol. 92, No. 3, pp. 401–409.

The text was submitted by the authors in English.

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Grigoriev, P.G., Molchanov, S.A. On decoupling of functions of normal vectors. Math Notes 92, 362–368 (2012). https://doi.org/10.1134/S0001434612090088

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  • DOI: https://doi.org/10.1134/S0001434612090088

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