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Determinantal point processes in the plane from products of random matrices

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arxiv 1308.6817 v3 pith:AIYOQGSU submitted 2013-08-30 math.PR math-phmath.MP

Kartick Adhikari , Nanda Kishore Reddy , Tulasi Ram Reddy , Koushik Saha This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords matricesproductrandomcalculatedensityderivedeterminantaleigenvalues
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abstract

We show the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of $k$ independent $n\times n$ matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

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  1. Products of Complex Rectangular and Hermitian Random Matrices

    math.PR 2019-08 conditional novelty 7.0 of 10

    A new spherical transform with sign parameters gives the joint eigenvalue density and kernels for products of Pólya ensembles with Hermitian matrices.

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