Spectral densities of singular values of products of Gaussian and truncated unitary random matrices

Neuschel T (2020)
Random Matrices: Theory and Applications 9(4): 2050014.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We study the densities of limiting distributions of squared singular values of high-dimensional matrix products composed of independent complex Gaussian (complex Ginibre) and truncated unitary matrices which are taken from Haar distributed unitary matrices with appropriate dimensional growth. In the general case, we develop a new approach to obtain complex integral representations for densities of measures whose Stieltjes transforms satisfy algebraic equations of a certain type. In the special cases in which at most one factor of the product is a complex Gaussian, we derive elementary expressions for the limiting densities using suitable parameterizations for the spectral variable. Moreover, in all cases we study the behavior of the densities at the boundary of the spectrum.
Stichworte
Random matrix theory; products of random matrices; spectral density; singular values; free multiplicative convolution
Erscheinungsjahr
2020
Zeitschriftentitel
Random Matrices: Theory and Applications
Band
9
Ausgabe
4
Art.-Nr.
2050014
ISSN
2010-3263
eISSN
2010-3271
Page URI
https://pub.uni-bielefeld.de/record/2945602

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Neuschel T. Spectral densities of singular values of products of Gaussian and truncated unitary random matrices. Random Matrices: Theory and Applications. 2020;9(4): 2050014.
Neuschel, T. (2020). Spectral densities of singular values of products of Gaussian and truncated unitary random matrices. Random Matrices: Theory and Applications, 9(4), 2050014. doi:10.1142/S2010326320500148
Neuschel, T. (2020). Spectral densities of singular values of products of Gaussian and truncated unitary random matrices. Random Matrices: Theory and Applications 9:2050014.
Neuschel, T., 2020. Spectral densities of singular values of products of Gaussian and truncated unitary random matrices. Random Matrices: Theory and Applications, 9(4): 2050014.
T. Neuschel, “Spectral densities of singular values of products of Gaussian and truncated unitary random matrices”, Random Matrices: Theory and Applications, vol. 9, 2020, : 2050014.
Neuschel, T.: Spectral densities of singular values of products of Gaussian and truncated unitary random matrices. Random Matrices: Theory and Applications. 9, : 2050014 (2020).
Neuschel, Thorsten. “Spectral densities of singular values of products of Gaussian and truncated unitary random matrices”. Random Matrices: Theory and Applications 9.4 (2020): 2050014.