3 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…

Hiraga–Ichino–Ikeda Plancherel density conjecture. Define

Plancherel dimension-ratio decay conjecture. There exists $\alpha>0$ such that, for all $s$,