2 problems

Let $\lambda^{(n)}$ be a random Young diagram with $n$ boxes distributed according to the Plancherel measure. Let $K_{\lambda^{(n)}}$ be its transition-measure distribution functio…

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.…