10 problems

Let $\mu\in\mathcal P(\mathbb C)$ be a probability measure on $\mathbb C$, let $(X_i)_{i\in\mathbb N}$ be independent and identically distributed random variables with law $\mu$, a…

Let $k,l\ge 2$ and let $\pi\in\mathcal{P}([0,1]^k\times[0,1]^l)$ be a multivariate distribution. Multivariate adapted copula rate conjecture. Consistency should still hold, while t…

Let $D\geq 2$. For the unit cube $[0,1]^D$ with its $\ell^{\infty}$ metric and an absolutely continuous measure whose density is bounded away from both $0$ and $\infty$, the paper…

Let $(\mathfrak{X},d,\mu)$ be a metric Polish probability space. Equivalence conjecture. The space $(\mathfrak{X},d,\mu)$ is asymptotically average-case approximable if and only if…

Let $(\mathfrak{X},d,\mu)$ be a metric probability space, where $\mathfrak{X}$ is a compact, connected, $D$-dimensional Riemannian manifold, $d$ is its geodesic distance, and $\mu$…

Let $(\mathfrak{X},d,\mu)$ be a metric Polish probability space. The average-case bound refers to high-probability approximation of expectations of Lipschitz functions by empirical…

Let $\mu$ be a sub-Gaussian probability measure, and let $\mu_n$ be its empirical measure. For a smoothing parameter $\sigma>0$, write $\gamma_\sigma$ for the centered Gaussian mea…

For each zero $Z_{k,n}$ of a random polynomial $p_n$, let $ζ_{k,n}$ be a nearest critical point and define … Here $\mathcal M_1(\mathbb C)$ denotes the space of probability measure…

Let $\mu$ be a probability measure, and let $\hat \mu_n$ denote the empirical measure formed from $n$ independent samples from $\mu$. Consider other measures produced by reasonable…

Let $(X_i)_{i=1}^{\infty}$ be the Kakutani process on $[0,1]$, in which the $n$-th point is selected uniformly from the largest interval among the current gaps, and let … be its em…