Gap probabilities in the finite and scaled cauchy random matrix ensembles

Nonlinearity

Volumn 13, Issue 6, 2000, Pages 1965-1986

  Witte, N S ^a   Forrester, P J ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034311207     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/13/6/305     Document Type: Article

References (14)

1. Adler M, Forrester P J, Nagao T and van Moerbeke P 1999 Classical skew orthogonal polynomials and random matrices Preprint solv-int/9907001
2. Askey R 1989 Beta Integrals and the Associated Orthogonal Polynomials (Lecture Notes in Mathematics vol 1395) (Berlin: Springer) pp 84-121
3. Cosgrove C M and Scoufis G 1993 Painlevé classification of a class of differential equations of the second order and second degree Stud. Appl. Math. 88 25-87
4. Forrester P J 2000 Log gases and random matrices, in preparation
5. Forrester P J and Odlyzko A M 1996 Gaussian unitary ensemble eigenvalues and Riemann ζ function zeros: a nonlinear equation for a new statistic Phys. Rev. E 54 4493-5
6. Forrester P J and Rains E M 1999 Inter-relationships between orthogonal, unitary and symplectic matrix ensembles Preprint solv-int/9907008
7. Forrester P J and Witte N S 2000 Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles Lett. Math. Phys.
8. Haine L and Semengue J P 1999 The Jacobi polynomial ensemble and the Painlevé VI equation J. Math. Phys. 40 2117-34
9. Its A R, Izergin A G, Korepin V E and Slavnov N A 1990 Differential equations for quantum correlation functions Int. J. Mod. Phys. B 4 1003-37
10. Jimbo M, Miwa T, Mori Y and Sato M 1980 Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent Physica D 1 80-158
11. Nagao T and Slevin K 1993 Nonuniversal correlations for random matrix ensembles J. Math. Phys. 34 2075-85
12. Romanovski V 1929 Calcul des probabilities - sur quelques classes nouvelles de polynomes orthogonaux C. R. Seances Acad. Sci. 188 1023-5
13. Tracy C A and Widom H 1994 Fredholm determinants, differential equations and matrix models Commun. Math. Phys. 163 33-72
14. Witte N S, Forrester P J and Cosgrove C M 2000 Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles Nonlinearity 13 1439-64