2020/07/20 by Nick Halmagyi, Halmagyi, Nick, Shailesh Lal +1 · 1 citation
Mathematics · Computer Science · #Random Matrices and Applications #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models
paper · pdf · doi:10.48550/arxiv.2007.10181
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.