5 problems

Asymptotic independence conjecture. For every $x,y\in\mathbb{R}$,

Let $\mathbf{M}$ be the random matrix from theorem $\mathrm{th:sym}$, with eigenvalues ordered so that $\lambda_1(\mathbf{M})$ is the dominant eigenvalue and…

Eigenvalue-variance conjecture. As $L\to\infty$,

Most stably singular initial-condition conjecture. Among all initial conditions for Dyson Brownian motion, those maximizing $R^{(1)}_\beta(0)$ are precisely

Let $U$ be an $N\times N$ random matrix from the circular unitary ensemble with eigenvalues $\{e^{i\theta_j}\}_{1\le j\le N}$, where $0\le \theta_1\le\dots\le\theta_N<2\pi$. Choose…