4 problems

Let $\widetilde{\lambda}_n$ denote the scaled largest-eigenvalue fluctuation in the GUE minor process. Paquette–Zeitouni's conjecture. The liminf has an almost-sure limiting consta…

Consider integrable last passage percolation on $\mathbb{Z}^2_{\geq 0}$ with independent exponential or geometric site weights, and let $\alpha_{\mathrm{sup}}$ satisfy…

Let $\mathfrak{h}_t$ denote the KPZ height fluctuation at time $t$, under initial data more general than the narrow wedge, and consider its large peaks and valleys. KPZ scaling con…

Approximation conjecture. The constants used in the theorems are good approximations of the corresponding quantities $\mathbb{E}[Y_n]$ and $\sqrt{\operatorname{Var}(Y_n)}$.