4 problems

Let $\mathcal{J}_{a}^{\beta}$ denote the stochastic Bessel operator in its original form, and let $\tilde{\mathcal{J}}_{a}^{\beta}$ denote its Liouville normal form. Consider type…

Let $k$ be a positive integer, and let $\beta$ be the parameter of the stochastic Airy operator and of the soft edge distribution. Stochastic Airy soft-edge conjecture. The $k$th l…

Poisson-limit conjecture. When $a\to\infty$, the rescaled point process $\mathcal{M}_a$ converges towards a Poisson point process.

Universality conjecture. The operator $H_{n,k}$ converges in the sense of Theorem (i) to