Universal microscopic correlation functions for products of independent Ginibre matrices

  title={Universal microscopic correlation functions for products of independent Ginibre matrices},
  author={Gernot Akemann and Zdzislaw Burda},
  journal={arXiv: Mathematical Physics},
We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of the product matrix is found to be given by a determinantal point process as in the case of a single Ginibre matrix, but with a more complicated weight given by a Meijer G-function depending on n. Using the method of orthogonal polynomials we compute all… 
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