2 problems

Let $0<\varepsilon<1$. Let $B\subset\mathbb{R}^d$ be a ball of radius $1/\sqrt n$, where $d$ may be as large as $\log n$. Suppose vectors…

Unitary near-invariance conjecture. An analogous near-invariance result should hold for arbitrary unitary matrices under this relaxed condition, with the exceptional matrices broad…