8 problems

$O(1/m)$ convergence-rate conjecture. The rate of convergence of this total variation distance should be further improved to $O(1/m)$.

Diaconis–Hicks conjecture. The rate of convergence of $\|Q_{n,1}-{\rm Uni}_n\|_{\mathrm{TV}}$ to zero is $O(1/\sqrt{n})$. This conjecture concerns the asymptotic approach to unifor…

Let $\theta_n$ be the statistic computed from two Gaussian random walks of length $n$, and let $\theta$ denote its limiting statistic. Write $r(n):=c n^{-1}$ for some constant $c$.…

Let a tensor product Markov chain be run for an increasing number of steps, and let its total variation distance denote the distance between its distribution after those steps and…

Let $\nu>0$, and let $F=I_2(f)$ belong to the second Wiener chaos with … Let $G(\nu)\sim\operatorname{CenteredGamma}(\nu)$. Two-sided total variation conjecture. There exist consta…

Total variation rate conjecture. In this setting, the estimate

Let $\bold{\Gamma}_n$ be an $n\times n$ Haar-invariant orthogonal matrix, let $\mathbf Z_n$ be its $p\times q$ upper-left submatrix, where $p=p_n$ and $q=q_n$ are positive integers…

Let $D({\bf p})$ denote the total variation discrepancy between the color distributions of a pair selected by the two matching procedures, and define … where the supremum ranges ov…