Infinite products of large random matrices and matrix-valued diffusion

Nuclear Physics B

Volumn 670, Issue 3, 2003, Pages 479-507

  Gudowska Nowak, Ewa ^a,b   Janik, Romuald A ^b   Jurkiewicz, Jerzy ^b   Nowak, Maciej A ^a,b  

^a GSI HELMHOLTZZENTRUM FÜR SCHWERIONENFORSCHUNG GMBH   (Germany)

^b JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

Diagrammatic expansion; Non Hermitian random matrix models; Products of random matrices

Indexed keywords

EID: 0141793863     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2003.08.012     Document Type: Article

References (54)

1. See, e.g. Mehta M.L. Random Matrices 1991 Academic Press New York
2. Porter C.E. Statistical Theories of Spectra: Fluctuations 1969 Academic Press New York
3. Dupuis N. Montambaux G. Phys. Rev. B 43 1991 14390
4. Guhr T. Mueller-Groeling A. Weidenmueller H.A. Phys. Rep. 299 1998 189
5. Haake F. et al. Z. Phys. B 88 1992 359
6. Lehmann N. Saher D. Sokolov V.V. Sommers H.-J. Nucl. Phys. A 582 1995 223
7. Ambjørn J. Jurkiewicz J. Makeenko Yu.M. Phys. Lett. B 251 1990 517
8. Ambjørn J. Chekhov L. Kristjansen C.F. Makeenko Yu. Nucl. Phys. B 404 1993 127
9. See Di Francesco P. Ginsparg P. Zinn-Justin J. Phys. Rep. 254 1995 1
10. Santhanam M.S. Patra P.K. Phys. Rev. E 64 2001 016102
11. Sengupta A.M. Mitra P.P. Phys. Rev. E 60 1999 3389
12. Caswell H. Matrix Population Models 2001 Sinauer Ass. Inc. Sunderland, MA
13. Mantegna R. Stanley H. An Introduction in Econophysics 2000 Cambridge Univ. Press Cambridge
14. Bouchaud J.P. Potters M. Theory of Financial Risks 2001 Cambridge Univ. Press Cambridge
15. Crisanti A. Paladin G. Vulpiani A. Products of Random Matrices in Statistical Physics 1993 Springer-Verlag Berlin
16. Beenakker C.W.J., in: Fukuyama H. Ando T. (Eds.), Transport Phenomena in Mesoscopic Systems Springer Series Solid-State Sciences 109 1992 Springer Berlin
17. Wang X.R. J. Phys. A 29 1996 3053
18. Diakonos F.K. Pingel D. Schmelcher P. Phys. Rev. E 62 2000 4413
19. de Oliveira M.J. Petri A. Phys. Rev. E 53 1996 2960
20. Tse D. Zeitouni O. IEEE Trans. Inform. Theory 46 2000 172
21. Barnsley M.F., in: Peitgen H.O. Saupe D. (Eds.), The Science of Fractal Images 1988 Springer-Verlag Berlin
22. Telatar I.E. Eur. Trans. Telecommun. 10 1999 585
23. Müller R.R. IEEE Trans. Inform. Theory 48 2002 2495
24. Taylor H.M. Karlin S. An Introduction to Stochastic Modeling 3rd Edition 1998 Academic Press New York
25. Jackson A.D. Lautrup B. Johansen P. Nielsen M. Phys. Rev. E 66 2002 066124
26. In preparation
27. Brézin E. Zee A. Phys. Rev. E 49 1994 2588
28. Brézin E. Zee A. Nucl. Phys. B 453 1995 531
29. Brézin E. Hikami S. Zee A. Universal correlations for deterministic plus random Hamiltonians hep-th/9412230
30. 't Hooft G. Nucl. Phys. B 75 1974 464
31. Janik R.A. Nowak M.A. Papp G. Wambach J. Zahed I. Phys. Rev. E 55 1997 4100
32. Janik R.A. Nowak M.A. Papp G. Zahed I. Nucl. Phys. B 501 1997 603; A different, but equivalent approach was also developed by [28].
33. Feinberg J. Zee A. Nucl. Phys. B 501 1997 643
34. Feinberg J. Zee A. Nucl. Phys. B 504 1997 579
35. Chalker J.T. Jane Wang Z. Phys. Rev. Lett. 79 1997 1797
36. Y.V. Fyodorov, H.-J. Sommers, unpublished
37. E. Wigner, Canad. Math. Congr. Proc. Univ. Toronto Press p.174 and other papers reprinted
38. Porter C.E. (Ed.), Statistical Theories of Spectra: Fluctuations 1965 Academic Press New York 1991.
39. Mehta M.L. Random Matrices 1991 Academic Press New York
40. Ginibre J. J. Math. Phys. 6 1965 440
41. Girko V.L. Spectral Theory of Random Matrices 1988 Nauka Moscow
42. Fyodorov Y.V. Sommers H.-J. J. Math. Phys. 38 1997 1918
43. Fyodorov Y.V. Khoruzhenko B.A. Sommers H.-J. Phys. Lett. A 226 1997 46
44. Sommers H.-J. Crisanti A. Sompolinsky H. Stein Y. Phys. Rev. Lett. 60 1988 1895
45. Janik R.A. Noerenberg W. Nowak M.A. Papp G. Zahed I. Phys. Rev. E 60 1999 2699
46. Gudowska-Nowak E. Papp G. Brickmann J. Chem. Phys. 232 1998 247
47. Gudowska-Nowak E. Papp G. Brickmann J. J. Phys. Chem. A 102 1998 9554
48. de Oliveira M.J. Petri A. Phys. Rev. E 53 1996 2960
49. Goldhirsch I. Sulem P.-L. Orszag S.A. Physica D 27 1987 311
50. Hatano N. Nelson D.R. Phys. Rev. Lett. 77 1996 570
51. Voiculescu D. Invent. Math. 104 1991 201
52. Voiculescu D.V. Dykema K.J. Nica A. Free Random Variables 1992 American Mathematical Society Providence, RI
53. Speicher R. Math. Ann. 298 1994 611
54. Biane Ph. Speicher R. Ann. Inst. H. Poincaré PR 37 5 2001 581