2 problems

Let $\lambda_{\max}^{(N)}(t)$ be the largest eigenvalue of an $N\times N$ matrix undergoing Dyson's Brownian motion with parameter $\beta=1$. Let ${\cal A}_{\rm 1}$ denote the Airy…

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