Asymptotic properties of large random matrices with independent entries

Journal of Mathematical Physics

Volumn 37, Issue 10, 1996, Pages 5033-5060

  Khorunzhy, Alexei M ^a   Khoruzhenko, Boris A ^a,b   Pastur, Leonid A ^a,c  

^a B VERKIN INSTITUTE FOR LOW TEMPERATURE PHYSICS AND ENGINEERING   (Ukraine)

^b QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^c UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030494613     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531589     Document Type: Article

References (37)

1. N.-M. Mehta, Random matrices, 2nd ed. (Academic, New York, 1991).
2. T. Brody, J. Flores, J. French, P. Mello, A. Pandey, and S. Wong, Rev. Mod. Phys. 53, 385 (1981).
3. J.-L. Pichard, in Quantum Cogerence in Mesoscopic Systems, edited by B. Kramer (Plenum, New York, 1991).
4. O. Bohigas, in Chaos and Quantum Physics, edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam, 1991).
5. Y. V. Fyodorov and A. D. Mirlin, Int. J. Mod. Phys. B 8, 3795 (1994).
6. D. Bessis, C. Itzykson, and J. Zuber, Adv. Appl. Math. 1, 109 (1980).
7. K. Demetrefi, Int. J. Mod. Phys. A 8, 1185 (1993).
8. P. Di Francesco, P. Ginsparg, and J. Zinn-Justin, Phys. Rep. 254, 1 (1995).
9. G. Cicuta, in Low Dimensional Topology and Quantum Field Theory, edited by H. Osborn (Plenum, New York, 1993).
10. D. J. Gross and T. Piran, Two Dimensional Quantum Gravity and Random Surfaces (World Scientific, Singapore, 1992).
11. F. J. Dyson, J. Math. Phys. 13, 90 (1972).
12. R. Kamien, H. Politzer, and M. Wise, Phys. Rev. Lett. 60, 1995 (1988).
13. L. A. Pastur, Lett. Math. Phys. 25, 259 (1992).
14. E. Brezin and A. Zee, Nucl. Phys. B 402, 613 (1993).
15. G. Hackenbroich and H. A. Weidenmüller, Phys. Rev Lett. 74, 4118 (1995).
16. L. A. Pastur and M. V. Shcherbina, J. Stat. Phys. (to be published).
17. E. Wigner, Ann. Math. 57, 325 (1958).
18. A. M. Khorunzhy and L. A. Pastur, Commun. Math. Phys. 153, 605 (1993).
19. B. A. Khoruzhenko, W. Kirsch, and L. A. Pastur, J. Phys. A 27, 2527 (1994).
20. A. M. Khorunzhy, W. Kirsch, and L. A. Pastur, Preprint ILT-4-93, B. I. Verkin Institute for Low Temperature, Kharkov, 1993.
21. A. M. Khorunzhy, B. A. Khoruzhenko, L. A. Pastur, and M. V. Shcherbina, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic, London, 1992), Vol. 15.
22. A.D. Mirlin and Y.V. Fyodorov, J. Phys. A 24, 227 (1991).
23. L. A. Pastur, Theor. Math. Phys. 10, 67 (1972).
24. V. L. Girko, Spectral Theory of Random Matrices (Nauka, Moscow, 1988) (in Russian).
25. In fact, in Ref. 23 a somewhat different and stronger form of condition (1.6) was used.
26. M. Reed and B. Simon, Methods of Modern Mathematical Physics (Academic, New York, 1978), Vol. 4.
27. V. A. Marchenko and L. A. Pastur, Math. USSR-sb 1, 457 (1967).
28. F. A. Berezin, Theor. Math. Phys. 17, 1163 (1973).
29. J. J. M. Verbaarschot, H. A. Weidenmüller, and M. R. Zirnbauer, Ann. Phys. 153, 367 (1984).
30. R. Opermann and F. Wegner, Z. Phys. B 34, 327 (1979).
31. A. M. Khorunzhy, B. A. Khoruzhenko, and L. A. Pastur, J. Phys. A 28, L31 (1995).
32. E. Lukacs, Characteristic Functions, 2nd ed. (Griffin, London, 1970).
33. L. A. Pastur, in "Mathematical Physics," Proceedings of the Tenth Congress in Mathematical Physics, edited by K. Smudgen (Springer, Heidelberg, 1992).
34. J. B French, P. A. Mello, and A. Pandey, Ann. Phys. 113, 277 (1978).
35. A. Pandey, Ann. Phys. 134, 110 (1981).
36. L. A. Pastur, A. M. Khorunzhy, and V. Vasilchuk, Dopovidi Acad Nauk Ukrainy 2, 25 (1995) (in Russian).
37. A. M. Khorunzhy, Rand. Oper. Stoch. Equations 2, 163 (1994).