7 problems

Let $X\sim\mathcal{N}_{v}(0,\Lambda)$, where $\Lambda=\operatorname{diag}(\lambda)$, and let … be the Euclidean ball of radius $\rho$. Consider the covariance matrix of the vector…

Eigenvalue bound conjecture. These eigenvalues satisfy

Let $T_1(Y)$ be the statistic in the separability test, and let $\gamma_0$ and $E_+$ be the quantities defined in the paper's equation (sec4.3.eq3). Let $TW_1$ denote the Tracy–Wid…

Let $\Sigma_1$ and $\Sigma_2$ be the covariance matrices, and let $H$ be their joint limiting spectral distribution. For any $n_1,n_2\in\mathbb{N}$ and every selection of non-negat…

Let $\Sigma_n$ be the covariance matrix of the length power functionals in the subcritical regime, for $n\geq 2$, with eigenvalues $\lambda_1\leq\ldots\leq\lambda_n$. Distinct-eige…

Large-system consistency conjecture. In this joint limit, $\widehat{k}$ is a consistent estimator of $k_{\mathrm{eff}}(c\mid {\bf R})$.

Classical consistency conjecture. With $n$ fixed and $m\to\infty$, $\widehat{k}$ is a consistent estimator of the true number of signals $k$.