Decoupling inequalities for multilinear forms in independent symmetric random variables (Q1081956)

Let \(\tilde X=(\tilde X_ 1,\tilde X_ 2,...)\) be an independent copy of a sequence \(X=(X_ 1,X_ 2,...)\) of independent symmetric random variables. Let B be a symmetric bilinear form on \({\mathbb{R}}^{{\mathbb{N}}}\) whose matrix \(a=(a_{ij})\) with respect to the standard basis of \({\mathbb{R}}^{{\mathbb{N}}}\) satisfies \(a_{kk}=0\) for all k and \(a_{kj}=0\) for all but finitely many pairs (k,j). The aim of this paper is to establish the inequality \[ cE| B(X,X)|^ p\leq E| B(X,\tilde X)|^ p \] for \(1\leq p<\infty\).