6 problems

Fix $z\in[0,1]$. Let $(u_0,v_0)=(\operatorname{RSK\ cos}z,\operatorname{RSK\ sin}z)$ be the corresponding point on the Logan--Shepp--Vershik--Kerov limit curve $\Omega_*$. For i.i.…

Let $\rho_-$ and $\rho_+$ be the left and right Bernoulli densities for the TASEP, let $\bar h(y)$ be the hydrodynamic limiting height profile, and let $h_t(j)$ be the height at ti…

Let $d\ge 2$ and consider the facilitated exclusion process (FEP), with critical density $\rho_c$ and stationary measure $\nu_\rho$. Write $\delta=\rho_c-\rho>0$, and let…

GUE Tracy–Widom fluctuation conjecture. There are functions $J:\mathbb{R}\to\mathbb{R}$ and $\sigma:\mathbb{R}\to\mathbb{R}$ such that

Let $\mathsf{SG}$ be the Sierpinski gasket graph, let $\mathcal{B}_n$ be the graph-metric ball of radius $n$, and let $\mathcal{I}_{|\mathcal{B}_n|}$ be the internal DLA cluster fo…

Let $SG$ be the graphical Sierpinski gasket, let $o$ be its source vertex, and let $B_o(n)$ denote the graph-metric ball of radius $n$ centered at $o$. Write…