Fine structure of moments of the KMK transform of the Poissonized   Plancharel measure
  We consider asymptotics behavior of Poissonized Plancharel measures as the poissonization parameter $N$ goes to infinity. Recently Moll proved a convergent series expansion for statistics of a measure $\mu_\lambda$ which is the Kerov-Markov-Krein transform of the signed measure on corners a Jack-random partition $\lambda$. The measure $\mu_\lambda$ is of interest because it behaves in some ways like the empirical measure on eigenvalues of a GUE-random matrix. We prove for the Poissonized Plancharel case that the large $N$ series for moments of $\mu_\lambda$ have a recursive structure as rational expressions in the generating function for Catalan numbers. We discuss the analogy between our result and the fine structure of moments of the GUE. 
Patrick Waters
math.CO math.PR