3 problems

Consider the spiked Wigner inference problem with signal-to-noise parameter $\beta_{\bM}$ and threshold $\beta_{\bM}$ as used in the paper. Let $\beta_{\bM}$ denote the scaled post…

Uniform stable approximation conjecture. The sequence $\boldsymbol{\Psi}_{P}$ is a stable approximation for $\mathcal{A}_{P}$: there exist $s=s(P)\geq 0$ and $C=C(P)\geq 0$ such th…

Let $[n]=\{1,\ldots,n\}$, let $\bm{A}_1,\ldots,\bm{A}_n$ be positive semidefinite matrices, and let $k$ be a positive integer. For a function of an ordered $k$-tuple, define … and…