An application of Brascamp-Lieb's inequality

TL;DR

This paper applies Brascamp-Lieb's inequality to derive new decoupling inequalities for Gaussian vectors and stationary cyclic Gaussian processes, extending previous results with advanced mathematical tools.

Contribution

It introduces novel decoupling inequalities for Gaussian processes using Brascamp-Lieb's inequality and the strong Szego limit theorem, broadening the scope of prior work.

Findings

New decoupling inequalities for Gaussian vectors

Extended results for stationary cyclic Gaussian processes

Application of strong Szego limit theorem in this context

Abstract

We use Brascamp-Lieb's inequality to obtain new decoupling inequalities for general Gaussian vectors, and for stationary cyclic Gaussian processes. In the second case, we use a version by Bump and Diaconis of the strong Szego limit theorem. This extends results of Klein, Landau and Shucker.