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Determinantal point processes in the plane from products of random matrices

Adhikari, Kartick and Reddy, Nanda Kishore and Reddy, Tulasi Ram and Saha, Koushik (2016) Determinantal point processes in the plane from products of random matrices. In: ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 52 (1). pp. 16-46.

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Official URL: http://dx.doi.org/10.1214/14-AIHP632

Abstract

We show that 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 x 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.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the INST MATHEMATICAL STATISTICS, 3163 SOMERSET DR, CLEVELAND, OH 44122 USA
Keywords: Determinantal point process; Eigenvalues; Empirical spectral distribution; Limiting spectral distribution; Haar measure; QR decomposition; Random matrix; RQ decomposition; Generalized Schur decomposition; Unitary matrix; Wedge product
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 18 Feb 2016 06:20
Last Modified: 18 Feb 2016 06:20
URI: http://eprints.iisc.ernet.in/id/eprint/53268

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