Statistics of real eigenvalues in Ginibre's ensemble of random real matrices

Physical Review Letters

Volumn 95, Issue 23, 2005, Pages

  Kanzieper, Eugene ^a   Akemann, Gernot ^b  

^a HOLON INSTITUTE OF TECHNOLOGY   (Israel)

^b BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DYSON INTEGRATION THEOREM; GAUSSIAN RANDOM MATRIX; GINIBRE'S ORTHOGONAL ENSEMBLE; SYMMETRIC FUNCTIONS;

MATHEMATICAL TECHNIQUES; MATRIX ALGEBRA; PROBABILISTIC LOGICS; SPECTRUM ANALYSIS; STATISTICAL METHODS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 28844438273     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.95.230201     Document Type: Article

References (33)

1. J. Ginibre, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 6, 440 (1965). 10.1063/1.1704292
2. M.L. Mehta, Random Matrices (Elsevier, New York, 2004), 3rd ed.
3. Y.V. Fyodorov and H.-J. Sommers, J. Phys. A JPHAC5 0305-4470 36, 3303 (2003). 10.1088/0305-4470/36/12/326
4. T. Guhr, A. Müller-Groeling, and H.A. Weidenmüller, Phys. Rep. PRPLCM 0370-1573 299, 189 (1998). 10.1016/S0370-1573(97)00088-4
5. R. Grobe, F. Haake, and H.-J. Sommers, Phys. Rev. Lett. 61, 1899 (1988); PRLTAO 0031-9007 10.1103/PhysRevLett.61.1899
6. R. Grobe and F. Haake, Phys. Rev. Lett. 62, 2893 (1989). PRLTAO 0031-9007 10.1103/PhysRevLett.62.2893
7. H.-J. Sommers, A. Crisanti, H. Sompolinsky, and Y. Stein, Phys. Rev. Lett. 60, 1895 (1988); PRLTAO 0031-9007 10.1103/PhysRevLett.60.1895
8. H. Sompolinsky, A. Crisanti, and H.-J. Sommers, Phys. Rev. Lett. 61, 259 (1988). PRLTAO 0031-9007 10.1103/PhysRevLett.61.259
9. M. Timme, F. Wolf, and T. Geisel, Phys. Rev. Lett. 89, 258701 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.258701
10. M. Timme F. Wolf T. Geisel Phys. Rev. Lett. 92, 074101 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.074101
11. J. Kwapień, S. Drozdz, and A.A. Ioannides, Phys. Rev. E 62, 5557 (2000). PLEEE8 1063-651X 10.1103/PhysRevE.62.5557
12. G. Le Caër and J.S. Ho, J. Phys. A JPHAC5 0305-4470 23, 3279 (1990); 10.1088/0305-4470/23/14/025
13. G. Le Caër and R. Delannay, J. Phys. I (France) JPGCE8 1155-4304 3, 1777 (1993). 10.1051/jp1:1993215
14. K.B. Efetov, Phys. Rev. Lett. 79, 491 (1997); PRLTAO 0031-9007 10.1103/PhysRevLett.79.491
15. K.B. Efetov Phys. Rev. B PRBMDO 0163-1829 56, 9630 (1997); 10.1103/PhysRevB.56.9630
16. A.V. Kolesnikov and K.B. Efetov, Waves Random Media 9, 71 (1999). WRMEEV 0959-7174 10.1088/0959-7174/9/2/301
17. Y. Fyodorov, B. Khoruzhenko, and H.-J. Sommers, Phys. Rev. Lett. 79, 557 (1997). PRLTAO 0031-9007 10.1103/PhysRevLett.79.557
18. M. Stephanov, Phys. Rev. Lett. 76, 4472 (1996); PRLTAO 0031-9007 10.1103/PhysRevLett.76.4472
19. M.A. Halasz, J.C. Osborn, and J.J.M. Verbaarschot, Phys. Rev. D 56, 7059 (1997); PRVDAQ 0556-2821 10.1103/PhysRevD.56.7059
20. H. Markum, R. Pullirsch, and T. Wettig, Phys. Rev. Lett. 83, 484 (1999); PRLTAO 0031-9007 10.1103/PhysRevLett.83.484
21. G. Akemann and T. Wettig, Phys. Rev. Lett. 92, 102002 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.102002
22. A. Zabrodin, in Proceedings of the International Conference on Theoretical Physics (TH-2002), edited by, D. Iagolnitzer, V. Rivasseau, and, J. Zinn-Justin, (Birkhäuser Verlag, Basel, 2003).
23. M. Mineev-Weinstein, P.B. Wiegmann, and A. Zabrodin, Phys. Rev. Lett. 84, 5106 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.84.5106
24. O. Agam, E. Bettelheim, P. Wiegmann, and A. Zabrodin, Phys. Rev. Lett. 88, 236801 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.88.236801
25. N. Lehmann and H.-J. Sommers, Phys. Rev. Lett. 67, 941 (1991). PRLTAO 0031-9007 10.1103/PhysRevLett.67.941
26. A. Edelman, J. Multivariate Anal. JMVAAI 0047-259X 60, 203 (1997). 10.1006/jmva.1996.1653
27. M.L. Mehta and P.K. Srivastava, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 7, 341 (1966). 10.1063/1.1704938
28. E. Kanzieper, J. Phys. A JPHAC5 0305-4470 35, 6631 (2002). 10.1088/0305-4470/35/31/308
29. F.J. Dyson, Commun. Math. Phys. 19, 235 (1970). CMPHAY 0010-3616 10.1007/BF01646824 A Class of Polynomials in Search of a Definition, or the Symmetric Group Parameterized, " in Proceedings of the Workshop on Jack, Hall-Littlewood and Macdonald Polynomials, edited by, V.B. Kuznetsov, and, S. Sahi, (American Mathematical Society, Providence, RI, to be published).
30. E. Kanzieper and G. Akemann (unpublished).
31. T. Nagao and S.M. Nishigaki, Phys. Rev. D 63, 045011 (2001). PRVDAQ 0556-2821 10.1103/PhysRevD.63.045011
32. A. Borodin and E. Strahov, Commun. Pure Appl. Math. CPMAMV 0010-3640 58, 0001 (2005). 10.1002/cpa.20050
33. C.A. Tracy and H. Widom, J. Stat. Phys. 92, 809 (1998). JSTPSB 0022-4715 10.1023/A:1023084324803