6 problems

Let $G(n,d,p)$ be the spherical random geometric graph and let $G(n,p)$ be the Erdős–Rényi random graph. For probability distributions on a finite set, define total variation dista…

Let $\beta=k-\frac{1}{n_m}$, $p=n^{-\frac{1}{\beta}}$, and $q=n^{-\frac{km}{\beta}}$, with $n=n_m$. Let $\Gamma_{n,m,p}$ and $Y_{n,k,q}$ denote the two distributions defined in the…

Let $n\geq 2$, let $\Omega=(0,1)^n$, and consider functions with bounded Hessian--Schatten variation, together with the class $\operatorname{CPWL}(\Omega)$ of continuous piecewise-…

Linear-size approximation conjecture. As $n\in 2\mathbb{N}$ tends to infinity,

Let ${sf TDLA}0(n,{ sf Torus}(n^c))$ denote the finite-graph DLA tree with $n$ vertices rooted at $0$, and let ${bf dla}n$ denote the standard DLA tree with $n$ vertices. **The fin…

Let $C\subset\mathbb{R}^2$ be a bounded ellipse whose indicator function is an eigenfunction in the sense of the adaptive anisotropic total variation eigenfunction equation, and le…