5 problems

Wishart Gaussian product inequality conjecture.

Let $\mathfrak{X}$ be the Wishart random matrix in the setting of the cited theorem, partitioned into diagonal blocks $\mathfrak{X}_{ii}$ of widths $p_1,\ldots,p_d$. Wishart princi…

Let $p\in\mathbb{N}$, let $\alpha\in(p-1,\infty)$, and let $\Sigma\in\mathcal{S}_{++}^p$. Let $\mathfrak{X}\sim\mathcal{W}_p(\alpha,\Sigma)$ be a $p\times p$ Wishart random matrix,…

Let $W=(NQ)^{-1}$ be the Wishart matrix described above, and define $c_0(\mu_1,\dots,\mu_\ell)$ by … Here $\ell\geq 1$, $(\mu_1,\dots,\mu_\ell)\in\mathbb{N}^{\ell}$, and $C_\ell$ d…

Determinantal formula. There is a function $C(x)$ such that