A method to calculate correlation functions for β=1 random matrices of odd size

Journal of Statistical Physics

Volumn 134, Issue 3, 2009, Pages 443-462

  Forrester, Peter J ^a   Mays, Anthony ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Correlation functions; Ginibre ensemble; Pfaffian processes; Random matrices

Indexed keywords

EID: 61349193752     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9684-6     Document Type: Article

References (31)

1. M. Adler P.J. Forrester T. Nagao P. van Moerbeke 2000 Classical skew orthogonal polynomials and random matrices J. Stat. Phys. 99 1/2 141
2. G. Akemann E. Kanzieper 2007 Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem J. Stat. Phys. 129 1159 1231
3. Borodin, A., Sinclair, C.D.: Correlation functions of ensembles of asymmetric real matrices (2007). arXiv:0706.2670 [math-ph]
4. Borodin, A., Sinclair, C.D.: The Ginibre ensemble of real random matrices and its scaling limits (2008). arXiv:0805.2986 [math-ph]
5. N.G. De Bruijn 1955 On some multiple integrals involving determinants J. Indian Math. Soc. 19 133 151
6. F.J. Dyson 1962 Statistical theory of the energy levels of complex systems I J. Math. Phys. 3 1 140 156
7. F.J. Dyson 1970 Correlations between eigenvalues of a random matrix Commun. Math. Phys. 19 235 250
8. A. Edelman 1997 The probability that a random real Gaussian matrix has k real eigenvalues, related distributions, and the circular law J. Multivar. Anal. 60 203 232
9. A. Edelman E. Kostlan M. Shub 1994 How many eigenvalues of a random matrix are real? J. Am. Math. Soc. 7 1 247 267
10. Forrester, P.J.: Log gases and random matrices. Currently available at: http://www.ms.unimelb.edu.au/~matpjf/matpjf.html (forthcoming)
11. P.J. Forrester T. Nagao 2007 Eigenvalue statistics of the real Ginibre ensemble Phys. Rev. Lett. 99 050603
12. P.J. Forrester T. Nagao 2008 Skew orthogonal polynomials and the partly symmetric real Ginibre ensemble J. Phys. A 41 375003
13. K. Frahm J.-L. Pichard 1995 Magnetoconductance of ballistic chaotic quantum dots: A Brownian motion approach for the S-matrix J. Phys. I. 5 874
14. J. Ginibre 1965 Statistical ensembles of complex, quaternion and real matrices J. Math. Phys. 6 3 440
15. E. Kanzieper 2002 Eigenvalue correlations in Ginibre's non-Hermitean random matrices at β=4 J. Phys. A 35 6631 6644
16. A.M. Lane R.G. Thomas E.P. Wigner 1955 Giant resonance interpretation of the nucleon-nucleus interaction Phys. Rev. 98 3 639 701
17. N. Lehmann H.-J. Sommers 1991 Eigenvalue statistics of random real matrices Phys. Rev. Lett. 67 8 941 944
18. G. Mahoux M.L. Mehta 1991 A method of integration over matrix variables: IV J. Phys. I. 1 1093 1108
19. M.L. Mehta 1960 On the statistical properties of the level-spacings in nuclear spectra Nucl. Phys. 18 395 419
20. M.L. Mehta 1971 A note on correlations between eigenvalues of a random matrix Commun. Math. Phys. 20 245 250
21. M.L. Mehta 1976 A note on certain multiple integrals J. Math. Phys. 17 12 2198 2202
22. Mehta, M.L.: Random Matrices. Elsevier, Amsterdam (2004)
23. M.L. Mehta F.J. Dyson 1963 Statistical theory of the energy levels of complex systems V J. Math. Phys. 4 5 713 719
24. P. Shukla 2001 Non-Hermitian random matrices and the Calogero-Sutherland model Phys. Rev. Lett. 87 19 194102
25. C.D. Sinclair 2007 Averages over Ginibre's ensemble of random real matrices Int. Math. Res. Not. 2007 1 15 rnm015
26. Sinclair, C.D.: Correlation functions for β=1 ensembles of matrices of odd size (2008). arXiv:0811.1276 [math-ph]
27. H.-J. Sommers 2007 Symplectic structure of the real Ginibre ensemble J. Phys. A 40 F671
28. H.-J. Sommers W. Wieczorek 2008 General eigenvalue correlations for the real Ginibre ensemble J. Phys. A 41 405003
29. C.A. Tracy H. Widom 1998 Correlation functions, cluster functions and spacing distributions for random matrices J. Stat. Phys. 92 5/6 809 835
30. E.P. Wigner 1955 Characteristic vectors of bordered matrices with infinite dimensions Ann. Math. 62 3 548 564
31. Wigner, E.P.: Statistical properties of real symmetric matrices with many dimensions. In: Canadian Mathematical Congress Proceedings. University of Toronto Press, Toronto (1957)