Cedric Phillips

Two short proofs of incompatibility for correlation matrices

Let $P_d$ be the elliptope of $d \times d$ correlation matrices, and, for a standardised law $F$, let $S_d^F$ be the set of correlation matrices of random vectors with all margins $F$. We give two short proofs. First, an eleven-term representation of $|x|^4$ as a sum of fourth powers of linear forms on $\mathbb{R}^4$ y...