Geodesic
On Decoupling of Functions of Normal Vectors
Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 401-409

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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, Schur product
Mots-clés : Hermite polynomial, Hadamard product, covariance matrix. 
P. G. Grigor'ev; S. A. Molchanov. On Decoupling of Functions of Normal Vectors. Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 401-409. http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a7/
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