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Mathematical Notes

, Volume 92, Issue 3–4, pp 362–368 | Cite as

On decoupling of functions of normal vectors

  • P. G. GrigorievEmail author
  • S. A. Molchanov
Article
  • 76 Downloads

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.

Keywords

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

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.University of North CarolinaCharlotteUSA

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