Singularity dominated strong fluctuations for some random matrix averages

Communications in Mathematical Physics

Volumn 250, Issue 1, 2004, Pages 119-131

  Forrester, P J ^a   Keating, J P ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4744349420     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1121-8     Document Type: Article

References (25)

1. Berry, M.V.: Focusing and twinkling: critical exponents from catastrophes in non-Gaussian random short waves. J. Phys. A 10, 2061-2081 (1977)
2. Berry, M.V.: Universal power-law tails for singularity-dominated strong fluctuations. J. Phys. A 15, 2735-2749 (1977)
3. Berry, M.V., Keating, J.P.: Clusters of near degenerate levels dominate negative moments of spectral determinants. J. Phys. A 35, L1-L6 (2002)
4. Berry, M.V., Keating, J.P., Schomerus, H.: Universal twinkling exponents for spectral fluctuations associated with mixed chaology. Proc. R. Soc. A 456, 1659-1668 (2000)
5. Conrey, J.B., Farmer, D.W.: Mean values of L-functions and symmetry. Int. Math. Res. Notices 17, 883-908 (2000)
6. Conrey, J.B., Farmer, D.W., Keating, J.P., Rubinstein, M.O., Snaith, N.C.: Integral moments of zeta-and L-functions. Submitted to Proc. of the London Math.Soc.
7. Forrester, P.J.: Log-gases and Random Matrices, http://www.ms.unimelb. edu.au/~matpjf/mat-pjf.html, 2003
8. 2 quantum many body system. Nucl. Phys. B 416, 377-385 (1994)
9. Forrester, P.J.: Integration formulas and exact calculations in the Calogero-Sutherland model. Mod. Phys. Lett B 9, 359-371 (1995)
10. VI τ-functions, http://arXiv.org/abs/math-ph/0308036, 2003
11. Fyodorov, Y.V., Keating, J.P.: Negative moments of characteristic polynomials of random GOE matrices and singularity dominated strong fluctuations. J. Phys. A 36, 4035-4046 (2003)
12. Hughes, C.P., Keating, J.P., O'Connell, N.: On the characteristic polynomial of a random unitary matrix. Commun. Math. Phys. 220, 429-451 (2001)
13. e série 112, 257-304 (1988)
14. Johansson, K.: On random matrices from the compact classical groups. Ann. of Math. 145, 519-545 (1997)
15. Johansson, K.: On fluctuation of eigenvalues of random Hermitian matrices. Duke Math. J. 91, 151-204 (1998)
16. Kadell, K.W.J.: The Selberg-Jack symmetric functions. Adv. Math. 130, 33-102 (1997)
17. Kaneko, J.: Selberg integrals and hypergeometric functions associated with Jack polynomials. SIAM J. Math Anal. 24, 1086-1110 (1993)
18. Keating, J.P., Prado, S.D.: Orbit bifurcations and the scarring of wave functions. Proc. R. Soc. A 457, 1855-1872 (2001)
19. Keating, J.P., Snaith, N.C.: Random matrix theory and L-functions at s = 1/2. Commun. Math. Phys. 214, 91-110 (2000)
20. Keating, J.P., Snaith, N.C.: Random matrix theory and L (1/2 + it). Commun. Math. Phys. 214, 57-89 (2001)
21. Keating, J.P., Snaith, N.C.: Random matrices and L-functions. J. Phys. A 36, 2859-2881 (2003)
22. Macdonald, I.G.: Commuting differential operators and zonal spherical functions. In A.M. Cohen et al., editor, Algebraic Groups, Utrecht 1986, Vol. 1271 of Lecture Notes in Math., Heidelberg: Springer-Verlag, 1987, pp. 189-200
23. Macdonald, I.G.: Hall polynomials and symmetric functions. 2nd edition, Oxford: Oxford University Press, 1995
24. Szegö, G.: On certain Hermitian forms associated with the Fourier series of a positive function. Comm. Seminaire Math. de l'Univ. de Lund, tome supplémentaire, dédié à Marcel Riesz, 1952, pp. 228-237
25. Van, Z.: A class of generalized hypergeometric functions in several variables. Can J. Math. 44, 1317-1338 (1992)