Spectral density of generalized Wishart matrices and free multiplicative convolution.

  title={Spectral density of generalized Wishart matrices and free multiplicative convolution.},
  author={Wojciech Mlotkowski and Maciej A. Nowak and Karol A. Penson and Karol Życzkowski},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={92 1},
We investigate the level density for several ensembles of positive random matrices of a Wishart-like structure, W=XX(†), where X stands for a non-Hermitian random matrix. In particular, making use of the Cauchy transform, we study the free multiplicative powers of the Marchenko-Pastur (MP) distribution, MP(⊠s), which for an integer s yield Fuss-Catalan distributions corresponding to a product of s-independent square random matrices, X=X(1)⋯X(s). New formulas for the level densities are derived… 

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