5 problems

Let $\mathcal{A}$ be a unital C-algebra, let $0<\varepsilon<1$, and let $M,N\in\mathbb{N}$ and $\mathbf{x}_1,\dots,\mathbf{x}_M\in\mathcal{A}^N$. Modular Johnson–Lindenstrauss flat…

Let $Q_T$ be an orthogonal repeated averaging (ORA) process of length $T$ on $\operatorname{SO}(d)$, formed by repeatedly applying random coordinate-plane averaging rotations. Avro…

Let $Q_T$ be a Kac walk on $\operatorname{SO}(d)$, and let the target dimension be $O(\epsilon^{-2}\log n)$, corresponding to the $O(\epsilon^{-2}\log n)$-Stiefel manifold in $d$ d…

Let $Q_T$ be a Kac walk of length $T$ on $\operatorname{SO}(d)$, obtained by composing random coordinate-plane rotations. Given a set of $n$ points in $\mathbb{R}^{d}$ and an error…

Let $f(n,d,\varepsilon)$ denote the smallest $m$ such that every $n$-point subset of $\ell_2^d$ can be embedded into $\ell_2^m$ with distortion at most $1+\varepsilon$. Dimension-r…