Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices

Ipsen J (2015)
Journal of Physics A Mathematical and Theoretical 48(15): 155204.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Abstract / Bemerkung
We study the joint density of eigenvalues for products of independent rectangular real, complex and quaternionic Ginibre matrices. In the limit where the number of matrices tends to infinity, it is shown that the joint probability density function for the eigenvalues forms a permanental point process for all three classes. The moduli of the eigenvalues become uncorrelated and log-normal distributed, while the distribution for the phases of the eigenvalues depends on whether real, complex or quaternionic Ginibre matrices are considered. In the derivation for a product of real matrices, we explicitly use the fact that all eigenvalues become real when the number of matrices tends to infinity. Finally, we compare our results with known results for the Lyapunov exponents as well as numerical simulations.
Stichworte
products of matrices; random matrix theory; Lyapunov exponents
Erscheinungsjahr
2015
Zeitschriftentitel
Journal of Physics A Mathematical and Theoretical
Band
48
Ausgabe
15
Art.-Nr.
155204
ISSN
1751-8113
Page URI
https://pub.uni-bielefeld.de/record/2733378

Zitieren

Ipsen J. Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices. Journal of Physics A Mathematical and Theoretical. 2015;48(15): 155204.
Ipsen, J. (2015). Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices. Journal of Physics A Mathematical and Theoretical, 48(15), 155204. doi:10.1088/1751-8113/48/15/155204
Ipsen, J. (2015). Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices. Journal of Physics A Mathematical and Theoretical 48:155204.
Ipsen, J., 2015. Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices. Journal of Physics A Mathematical and Theoretical, 48(15): 155204.
J. Ipsen, “Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices”, Journal of Physics A Mathematical and Theoretical, vol. 48, 2015, : 155204.
Ipsen, J.: Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices. Journal of Physics A Mathematical and Theoretical. 48, : 155204 (2015).
Ipsen, Jesper. “Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices”. Journal of Physics A Mathematical and Theoretical 48.15 (2015): 155204.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar