15 problems

Let $u$ be a finite measure on $[0,1]$, and consider the operator deterministic equivalent under the paper's high-dimensional assumption and continuum MDE hypotheses. The proved r…

Let $u$ be a finite positive measure on $[0,1]$. The deterministic equivalent is established when $u$ is a finite discrete measure. Continuum-measure extension conjecture. Th…

Let $\mathcal{G}$ be a graph on $n$ vertices with non-abelian automorphism group $G=\operatorname{Aut}(\mathcal{G})$ of order $n$, and let $\mathbf{x}$ be a single observation of a…

Blind group selection consistency conjecture. The spectral-concentration selector is consistent at high signal-to-noise ratio:

Let $f: \mathbb{C}^M \to \mathcal{V}$ be a statistic and let $G$ act on $\mathbb{C}^M$ through a representation $\pi$. Define the effective group order by … for generic…

Let $M$ be a sufficiently smooth unknown manifold, and consider spectrum estimation for a weighted Laplace operator on $M$. Unknown-manifold rate conjecture. Lack of direct access…

Let $M$ be an unknown sufficiently smooth $d$-dimensional submanifold of $\mathbb{R}^D$. Aamari and Levrard's chart-based manifold estimators can be adapted to construct an estimat…

Let $Z(x,t)$ satisfy Condition B and the previous assumptions, and let $F_q({\Greekmath 0115}_m)$ and $\widehat{F}_q({\Greekmath 0115}_m)$ be the corresponding population and sampl…

Subspace-estimation condition conjecture. The condition

Let $\mathfrak{H}_{+,m}$ denote the cone of positive semidefinite Hermitian $m\times m$ matrices, let $\mathbb T^d$ be the $d$-dimensional torus, and let $\mathrm{d}M$ be a nonnega…

Let a spectrally sparse signal have spectral components estimated from $2m+1$ uniform temporal measurements, and let the distance between its spectral components be measured on the…

Let $c_0,\ldots,c_n$ be a positive covariance sequence and let $P$ be a positive numerator polynomial. Suppose there exists a rational covariance extension of the sought form with…

Let $\mathcal{S}=\{\omega_j:j\in\mathbb{Z}\}$ be a periodic support set on a lattice of spacing $\Delta$, with Rayleigh index $R_*$. Define … and let $\smin^2(\Phi^L)$ denote the c…

Let a line-spectral estimation problem be solved using atomic norm regularization, and let the regularization parameter denote the coefficient controlling the strength of that regu…

Consistency conjecture. The estimators of $H(t)$ and the corresponding functions, such as $\frac{1}{n}\operatorname{tr}\mathbf{T}_n^2$, obtained by the above method, are also consi…