Mixed Moments for the Product of Ginibre Matrices
arXiv:2007.10181v11 citations
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This provides theoretical insights into random matrix theory, but it is incremental as it extends known results to product ensembles.
The paper tackled the problem of characterizing the ensemble of products of complex Gaussian matrices by computing mixed moments, finding that at large matrix sizes they are described by non-crossing pairings weighted by Fuss-Catalan numbers.
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.