3 problems

Tracy–Widom GUE fluctuation conjecture. One has

Fix $t\in\mathbb Z$. In the half-space Beta random walk in random environment, define … for $x\in\mathbb Z_{\geqslant 0}$. Half-space Gamma-distribution conjecture. The limit exist…

Let $t\in\mathbb Z$ and consider the full-space Beta random walk in random environment. For each $x\in\mathbb Z$, let $\mathsf Z_t^{\mathbb Z}(x)$ denote the full-space point-to-li…