Squared chaotic random variables: new moment inequalities with applications

Abstract

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 generalisation, as well as a new analytical proof, of an estimate by Frenkel (2007), and also constitute a natural real counterpart to an inequality established by Arias-de-Reyna (1998) 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), as well as to obtain a novel probabilistic representation of the remainder in Hadamard inequality of matrix analysis.

22 pages

References in corpus (3)

• The plank problem for symmetric bodies
• Generalization of the Nualart-Peccati criterion
• Analytic and Probabilistic Problems in Discrete Geometry

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• Miscellaneous results related to the Gaussian product inequality conjecture for the joint distribution of traces of Wishart matrices
• A combinatorial proof of the Gaussian product inequality beyond the MTP${}_2$ case
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• Superconvergence phenomenon in Wiener chaoses
• Proof of Gaussian moment product conjecture
• Unlinking Theorem for Symmetric Quasi-convex Polynomials