Determinantal point processes in the plane from products of random matrices

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.

31 pages, 0 figure. Added a reference to the previous version

References in corpus (3)

• Products of Rectangular Random Matrices: Singular Values and Progressive Scattering
• On the Asymptotic Spectrum of Products of Independent Random Matrices
• Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)

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