Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem

Akemann G, Kanzieper E (2007)
J. Stat. Phys. 129(5-6): 1159-1231.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Akemann, GernotUniBi; Kanzieper, Eugene
Abstract / Bemerkung
In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95,230201 (2005); arXiv: math-ph/0507058], an exact solution was reported for theprobability "p_{n,k}" to find exactly "k" real eigenvalues in the spectrum ofan "n" by "n" real asymmetric matrix drawn at random from Ginibre's OrthogonalEnsemble (GinOE). In the present paper, we offer a detailed derivation of theabove result by concentrating on the proof of the Pfaffian integration theorem,the key ingredient of our analysis of the statistics of real eigenvalues in theGinOE. We also initiate a study of the correlations of complex eigenvalues andderive a formula for the joint probability density function of all complexeigenvalues of a GinOE matrix restricted to have exactly "k" real eigenvalues.In the particular case of "k=0", all correlation functions of complexeigenvalues are determined.
Erscheinungsjahr
2007
Zeitschriftentitel
J. Stat. Phys.
Band
129
Ausgabe
5-6
Seite(n)
1159-1231
ISSN
0022-4715
eISSN
1572-9613
Page URI
https://pub.uni-bielefeld.de/record/1978555

Zitieren

Akemann G, Kanzieper E. Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem. J. Stat. Phys. 2007;129(5-6):1159-1231.
Akemann, G., & Kanzieper, E. (2007). Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem. J. Stat. Phys., 129(5-6), 1159-1231. https://doi.org/10.1007/s10955-007-9381-2
Akemann, G., and Kanzieper, E. (2007). Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem. J. Stat. Phys. 129, 1159-1231.
Akemann, G., & Kanzieper, E., 2007. Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem. J. Stat. Phys., 129(5-6), p 1159-1231.
G. Akemann and E. Kanzieper, “Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem”, J. Stat. Phys., vol. 129, 2007, pp. 1159-1231.
Akemann, G., Kanzieper, E.: Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem. J. Stat. Phys. 129, 1159-1231 (2007).
Akemann, Gernot, and Kanzieper, Eugene. “Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem”. J. Stat. Phys. 129.5-6 (2007): 1159-1231.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Quellen

arXiv: math-ph/0703019

Suchen in

Google Scholar