Squared chaotic random variables: New moment inequalities with applications

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• 作者：Dominique Malicet^a ; ^{malicet@crans.org" class="auth_mail" title="E-mail the corresponding author} ; Ivan Nourdin^b ; ^{ivan.nourdin@uni.lu" class="auth_mail" title="E-mail the corresponding author} ; Giovanni Peccati^b ; ¹ ; ^{giovanni.peccati@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Guillaume Poly^c ; ^{guillaume.poly@univ-rennes1.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Gaussian vectors ; Hadamard inequality ; Variance inequalities ; Wiener chaos
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：270
• 期：2
• 页码：649-670
• 全文大小：444 K

文摘

We prove a new family of inequalities involving squares of random variables belonging to the Wiener chaos associated with a given Gaussian field. Our result provides a substantial generalization, as well as a new analytical proof, of an estimate by Frenkel (2007) [10], and also constitutes a natural real counterpart to an inequality established by Arias-de-Reyna (1998) [2] in the framework of complex Gaussian vectors. We further show that our estimates can be used to deduce new lower bounds on homogeneous polynomials, thus partially improving results by Pinasco (2012) [19], as well as to obtain a novel probabilistic representation of the remainder in Hadamard inequality of matrix analysis.