5 problems

Let $\boldsymbol{A}_i=\boldsymbol{O}_i\bar{\boldsymbol{A}}+\sigma\boldsymbol{W}_i$ be noisy point clouds, and consider the least-squares problem … The associated semidefinite relax…

Let $\boldsymbol{D}=\boldsymbol{Z}\boldsymbol{A}+\sigma\boldsymbol{W}$ be the signal-plus-noise data matrix, where $\boldsymbol{A}$ is the signal matrix, $\boldsymbol{Z}$ encodes t…

Let $\boldsymbol{A}\in\mathbb{R}^{d\times m}$ be an underlying point cloud, let $\boldsymbol{O}_i$ be unknown orthogonal matrices, and let $\boldsymbol{\mu}_i$ be shift parameters.…

Noise-bound improvement conjecture. A more involved argument should improve the upper bound on $\sigma$ in this corollary. The conjectured improvement is motivated by the stronger…

Let $\alpha_d$ be the expected average of the singular values of a $d\times d$ random matrix whose entries are independent and distributed as $\mathcal{N}(0,1/d)$. Its boundary val…