Michel Weber
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.
Michel Weber
This paper contains 5 sections, 10 theorems, 71 equations.
Theorem 1.2
Let $X=\{X_i, 1\le i\le n\}$ be a centered Gaussian vector such that ${\mathbb E \,} X_i^2={\sigma}_i^2>0$ for each $1\le i\le n$, and with positive definite covariance matrix $C$. Let $p$ be such that Then for any complex-valued measurable functions $f_1, \ldots, f_n$ such that $f_i\in L^p({\mathbb R})$, for all $1\le i\le n$, the following inequality holds true,
