Decoupling Inequalities and Decoupling Coefficients of Gaussian Processes

We use Brascamp-Lieb’s inequality to obtain new decoupling inequalities for general Gaussian vectors, and in particular for finite stationary Gaussian processes. In the second case, we provide an application using a version by Bump and Diaconis of the strong Szegö limit theorem. We obtain sharp estimates on the decoupling coefficient of remarkable classes of Gaussian processes.