Mixed Moments for the Product of Ginibre Matrices

Abstract

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.

29 pages

References in corpus (2)

• On the Asymptotic Spectrum of Products of Independent Random Matrices
• Biorthogonal Polynomials for Potentials of two Variables and External Sources at the Denominator

Cited by in corpus (1)

• Universality classes for purification in nonunitary quantum processes