Description
After reviewing the Plancherel measure on partitions and its relevance in combinatorics and (asymptotic) representation theory, I will introduce a class of multiplicative statistics of Poissonized Plancherel random partitions. Their study is motivated by connections to integrable systems (Toda equations) and to important stochastic growth models (polynuclear growth models).
In particular, with Mattia Cafasso and Matteo Mucciconi we tackled the asymptotic study of these statistics. Building on the log-gas structure of the Poissonized Plancherel measure we derived optimal shapes for Poissonized Plancherel random partitions (which generalize the celebrated Vershik-Kerov-Logan-Shepp density and exhibit new behaviors naturally described in terms of elliptic functions) as well as refined asymptotic expansions for the statistics themselves.