Moments of the characteristic polynomial in the three ensembles of random matrices

Journal of Physics A: Mathematical and General

Volumn 34, Issue 22, 2001, Pages 4627-4639

  Mehta, Madan Lal ^a   Normand, Jean Marie ^a  

^a CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039251933     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/22/304     Document Type: Article

References (14)

1. See e.g., Mehta M L 1989 Matrix Theory Les Editions de Physique, 91944 Les Ulis Cedex, France appendix A. 14
2. Mahoux G and Mehta M L 1991 A method of integration over matrix variables IV J. Physique (France) 1 1093-108
3. See e.g., Erdélyi A et al (ed) 1953 Higher transcendental functions (Bateman Manuscript Project vol 2) (New York: McGraw-Hill) section 10.3
4. Szegö G 1939 Orthogonal Polynomials (Providence, RI: American Mathematical Society) equation (2.2.10)
5. Eynard B 2000 Private communication and http://xxx.lanl.cond-mat/0012046
6. Brézin E and Hikami S 2000 Characteristic polynomials of random matrices Commun. Math. Phys. 214 111-35
7. Keating J P and Snaith N C 2000 Random matrix theory and ζ (1/2 + it) Commun. Math. Phys. 214 57-89
8. Keating J P and Snaith N C 2000 Random matrix theory and L-functions at s = 1/2 Commun. Math. Phys. 214 91-110
9. Hughes C P, Keating J P and O'Connell N 2000 Random matrix theory and the derivative of the Riemann zeta function Proc. R Soc. A 456 2611-27
10. See e.g., Mehta M L 1991 Random Matrices (New York: Academic) chapter 6.5 and appendix A. 18
11. de Bruijn N G 1955 On some multiple integrals involving determinants J. Ind. Math. Soc. 19 133-51
12. See e.g., Erdéyli A et al (ed) 1953 Higher transcendental functions (Bateman Manuscript Project vol 2) (New York: McGraw-Hill) pp 30-31 section 10.13
13. Forrester P J and Witte N S Application of the τ-function theory of Painlevé equations to random matrices: PIV, PII and GUE Preprint equation (4.43) and the paragraph following equation (4.44)
14. See also, Baker T H and Forrester P J 1997 The Calogero-Sutherland model and generalized classical polynomials Commun. Math. Phys. 188 175-216 around equations (5.30)-(5.33)