2 problems

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…