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Mixed Moments for the Product of Ginibre Matrices

Mathematical Physics 2020-07-21 v1 Statistical Mechanics High Energy Physics - Theory math.MP Machine Learning

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 NN, they are given by an enumeration of non-crossing pairings weighted by Fuss-Catalan numbers.

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Cite

@article{arxiv.2007.10181,
  title  = {Mixed Moments for the Product of Ginibre Matrices},
  author = {Nick Halmagyi and Shailesh Lal},
  journal= {arXiv preprint arXiv:2007.10181},
  year   = {2020}
}

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29 pages