6 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…

The flat PNG model has a height function whose fluctuations are governed by the GOE Tracy–Widom distribution $F_1$, the limiting distribution of the properly rescaled largest eigen…

Problem 4. For $j=1,\dots,k$, do the rescaled processes satisfy

Let $\beta>0$. In the two limiting results for the largest eigenvalues of the beta-Gaussian corners process and Dyson Brownian motion, respectively, the limits are obtained by firs…

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

Multilevel coupling generator conjecture. Iteratively applying the intertwining formulas should yield a coupling of the $\beta$-Dyson Brownian motions in dimensions $1,2,\ldots,N$…