MATH-PHJul 20, 2020
Mixed Moments for the Product of Ginibre MatricesNick Halmagyi, Shailesh Lal
We study the ensemble of a product of n complex Gaussian i.i.d. matrices. We find this ensemble is Gaussian with a variance matrix which is averaged over a multi-Wishart ensemble. We compute the mixed moments and find that at large $N$, they are given by an enumeration of non-crossing pairings weighted by Fuss-Catalan numbers.