3 problems

Let $U_r\in\mathbb{R}^{d\times r}$ be an orthonormal matrix, and let $\mathrm{Gr}(d,r)$ denote the Grassmann manifold of $r$-dimensional subspaces of $\mathbb{R}^d$. Define … as in…

Let $(\mathcal{X},Q,\pi)$ be a Markov chain with invariant measure $\pi$, and suppose that a concentration property with respect to the distance $d_{\mathcal{W}}$ holds with profil…

Let $A_{\theta}^{\infty}$ be the smooth noncommutative two-torus with canonical trace $\tau$, generated by unitaries $U,V$, and let…