Multiplicative Averages of Plancherel Random Partitions: Elliptic Functions, Phase Transitions, and Applications

Mattia Cafasso, Matteo Mucciconi, Giulio Ruzza

We consider random integer partitions $\lambda$ that follow the Poissonized Plancherel measure of parameter $t^2$. Using Riemann$-$Hilbert techniques, we establish the asymptotics of the…