Joint ICTP/SISSA Statistical physics seminar: "Product of free identically distributed R-diagonal random matrices"
(Jagellonian University, Krakow )
We show that the eigenvalue density of the product of n identically distributed R-diagonal random matrices from a given matrix ensemble is equal to the eigenvalue density of n-th power of a single matrix from this ensemble in the limit of infinite matrix size. Using this observation one can derive the limiting eigenvalue density of the product of n independent identically distributed matrices for non-Hermitian matrix ensembles with invariant measures. We discuss two examples: the product of n Girko-Ginibre matrices and the product of n truncated unitary matrices.
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