Physics – Mathematical Physics
Scientific paper
2007-03-05
J. Stat. Phys. 129 (2007) 1159-1231
Physics
Mathematical Physics
73 pages, 6 figures, 2 tables
Scientific paper
10.1007/s10955-007-9381-2
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 the probability "p_{n,k}" to find exactly "k" real eigenvalues in the spectrum of an "n" by "n" real asymmetric matrix drawn at random from Ginibre's Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof of the Pfaffian integration theorem, the key ingredient of our analysis of the statistics of real eigenvalues in the GinOE. We also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a GinOE matrix restricted to have exactly "k" real eigenvalues. In the particular case of "k=0", all correlation functions of complex eigenvalues are determined.
Akemann Gernot
Kanzieper Eugene
No associations
LandOfFree
Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-114012