Poisson statistics for the largest eigenvalues in random matrix ensembles

Lecture Notes in Physics

Volumn 690, Issue , 2006, Pages 351-364

  Soshnikov, Alexander ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749024750     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-34273-7_26     Document Type: Article

References (46)

1. L. Arnold: J. Math. Anal. Appl. 20, 262 (1967).
2. C.W.J. Beenakker: Rev. Mod. Phys., 69, 731, (1997).
3. G. Ben Arous, S. Péché: Commun. Pure Appl. Math., to appear, (2005).
4. M.V. Berry, M. Tabor: Proc. R. Soc. London Ser. A 356, 375 (1977).
5. B.V. Bronk: J. Math. Phys., 6, (1965).
6. A. Casati, L. Molinari, and F. Izrailev: Phys Rev. Lett. 64, 1851 (1990).
7. A. Casati and V.L. Girko: Rand. Oper. Stoch. Equations, 1, 15 (1991).
8. P. Cizeau, J.P. Bouchaud: Phys Rev E, 50, 1810 (1994).
9. Z. Cheng, J.L. Lebowitz and P. Major: Prob. Theo. Rel. Fields, 100, 253 (1994).
10. D.J. Daley, D. Vere-Jones: An Introduction to the Theory of Point Processes, vol.I, 2nd edn, (Springer, Berlin Heidelberg New York 2003).
11. P. Deift Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics, Vol. 3, New York, 1999.
12. Z. Füredi and J. Komlós: Combinatorica, 1, 233 (1981).
13. P. Forrester: Nucl. Phys. B, 402, 709 (1994).
14. Y.V. Fyodorov and G. Akemann: JETP Lett. 77, 438 (2003).
15. W. Feller: An Introduction to Probability Theory and Its Applications, Vol. II. 2nd edn. (John Wiley and Sons, Inc., New York, London, Sydney 1971).
16. Y.V.AFyodorov and H.-J.Sommers: J.Phys.A:Math.Gen. 36, 3303 (2003).
17. A. Guionnet: Ann. Inst. H. Poincare Probab. Statist. 38, 341 (2002).
18. I.A. Ibragimov, Yu.V. Linnik, Independent and Stationary Sequences of Random Variables, translation from the Russian edited by J.F.C. Kingman, (Wolters-Noordhoff Publishing, Groningen, 1971).
19. A.T. James: Ann. Math. Stat., 35, (1964).
20. K. Johansson: Commun. Math. Phys., 215, 683, (2001).
21. I.M. Johnstone: Ann. Stat., 29, 297 (2001).
22. J. Karamata: Mathematica (Cluj), 4, 38, (1930).
23. M.R. Leadbetter, G.Lindgren and H. Rootzén: Extremes and Related Properties of Random Sequences and Processes, (Springer-Verlag, New York 1983).
24. V.A. Marchenko, L.A. Pastur: Math. USSR-Sb. 1, 457, (1967).
25. J. Marklof: Annals of Mathematics, 158, 419, (2003).
26. J. Marklof: The Berry-Tabor conjecture. In: Proceedings of the 3rd European Congress of Mathematics, Barcelona 2000, (Progress in Mathematics 202 (2001)), pp 421-427.
27. M.L. Mehta: Random Matrices, (Academic Press, New York 1991).
28. N. Minami: Commun. Math. Phys., 177, 709, (1996).
29. S.A. Molchanov: Commun. Math. Phys. 78, 429, (1981).
30. S.A. Molchanov, L.A. Pastur and A.M. Khorunzhy: Theor. Math. Phys. 90, 108 (1992).
31. R.J. Muirhead, Aspects of Multivariate Statistical Theory, (Wiley, New York 1982).
32. L.A. Pastur: Teor. Mat. Fiz., 10, 102, (1972).
33. P. Sarnak: Values at integers of binary quadratic forms. In Harmonic Analysis and Number Theory (Montreal, PQ, 1996), CMS Conf. Proc. 21, (Amer. Math. Soc., Providence, RI, 1997), pp 181-203.
34. E. Seneta: Regularly Varying Functions, Lecture Notes in Mathematics, 508 (eds. A.Dold and B.Eckmann), (Springer, New York, 1976).
35. Ya. Sinai: Adv. Sov. Math., AMS Publ., 3, 199, (1991).
36. A. Soshnikov: Commun. Math. Phys., 207, 697, (1999).
37. A. Soshnikov: J. Stat. Phys., 108, 1033, (2002).
38. A. Soshnikov: Elec. Commun. Probab., 9, 82, (2004).
39. A. Soshnikov, Y.Fyodorov: To appear in J. Math Phys. (2005), arXiv preprint math.PR/0403425.
40. C.A. Tracy, H. Widom: Commun. Math. Phys., 159, 151, (1994).
41. C.A. Tracy, H. Widom: Commun. Math. Phys., 177, 724, (1996).
42. J.J. Verbaarschot and T. Wettig: Annu.Rev.Nucl.Part.Sci, 50, 343 (2000).
43. S.S. Wilks: Mathematical Statistics, (Princeton University Press, Princeton 1943).
44. E. Wigner: Ann. of Math., 62, 548, (1955).
45. E. Wigner: Ann. of Math., 67, 325, (1958).
46. E. Wigner: SIAM Rev., 9, 1, (1967).