4 problems

Electrostatic energy convergence conjecture. There exists a constant $b>0$ such that

Let $\mathcal{P}$ be an Apollonian gasket and let $\mathcal R\subset\mathbb C$ satisfy $\mu(\mathcal R)>0$. For $T>0$, let $F_{T,\mathcal R}(s)$ denote the pair correlation functio…

Let $Z$ be a spatial process with spectral density $f$ satisfying condition (f-cond), let $N_\varepsilon$ be a set of observations approaching the origin, and let $b(r)$ denote the…

Limiting domination number conjecture. As $n\to\infty$, the domination number satisfies