7 problems

Let $X_1,X_2,\ldots$ be identically distributed random variables, let $S_n$ denote their normalized sum, and let $D(S_n)$ be the squared Mallows-distance quantity used in the paper…

Let $\mathcal{X} \subseteq \mathbb{R}^d$, let $\nu$ have a density, and let $P$ and $Q$ be measures on $\mathcal{X}$ with densities bounded away from zero, satisfying…

Let $F$ and $G$ be unimodal distributions in the sense that their quantile functions are differentiable almost everywhere, with derivatives $(F^{-1})'$ and $(G^{-1})'$ decreasing f…

Improved multivariate indicator-function bound. The inequality above holds for all $m\geq1$.

Let $\alpha\in(1,2)$, and consider approximation of a $d$-dimensional stable law by the relevant normalized sums. The approximation rate is measured in $L^{1}$ or total variation d…

Let $t$ denote the intensity parameter and let $d$ tend to infinity. The Gaussian and Poisson limit theorems above require growth conditions on $t$ because of dimension-dependent f…

Let $n$ be the number of points in the Bernoulli process and let $p$ be its success probability. Write $\bar{d}_2$ for the metric used to compare the Bernoulli point-process distri…