4 problems

Let $\left\{\Gamma^{(\beta)}\right\}_{\beta\nearrow\infty}$ be any sequence of standard graphs, labeled by their first Betti numbers. For each $\Gamma^{(\beta)}$, choose arbitrary…

Let $\{\Gamma_{\vec{l}}^{(\beta)}\}_{\beta\nearrow\infty}$ be any sequence of standard graphs parameterized by their first Betti numbers, with each graph having rationally independ…

Let … be its nodal surplus random variable. Write $\operatorname{Var}(\sigma)$ for its variance. Al-Obeid–Band–Berkolaiko's conjecture. As $\to\infty$, … where the convergence is i…

Let a quantum graph be a metric graph with edge lengths, and let the nodal domains of an eigenfunction be the connected components of the complement of its zero set. Consider well-…