Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices

International Mathematics Research Notices

Volumn 2006, Issue , 2006, Pages

  Forrester, Peter J ^a   Rains, Eric M ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646404330     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/IMRN/2006/48306     Document Type: Article

References (22)

1. G. S. Ammar, W. B. Gragg, and L. Reichel, Constructing a unitary Hessenberg matrix from spectral data, Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms (Leuven, 1988) (G. H. Golub and P. van Dooren, eds.), NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., vol. 70, Springer, Berlin, 1991, pp. 385-395.
2. G. W. Anderson, A short proof of Selberg's generalized beta formula, Forum Mathematicum 3 (1991), no. 4, 415-417.
3. J. Baik and E. M. Rains, Algebraic aspects of increasing subsequences, Duke Mathematical Journal 109 (2001), no. 1, 1-65.
4. A. Borodin and G. Olshanski, Infinite random matrices and ergodic measures, Communications in Mathematical Physics 223 (2001), no. 1, 87-123.
5. A. L. Dixon, Generalizations of Legendre's formula KE′ - (K - E)K′ = 1/2π, Proceedings of the London Mathematical Society 3 (1905), 206-224.
6. I. Dumitriu and A. Edelman, Matrix models for beta ensembles, Journal of Mathematical Physics 43 (2002), no. 11, 5830-5847.
7. F. J. Dyson, Statistical theory of the energy levels of complex systems. III, Journal of Mathematical Physics 3 (1962), no. 1, 166-175.
8. P. J. Forrester, Log-Gases and Random Matrices, http://www.ms.unimelb.edu.au/~matpjf/matpjf.html.
9. P. J. Forrester, N. E. Frankel, and T. M. Garoni, Random matrix averages and the impenetrable Bose gas in Dirichlet and Neumann boundary conditions, Journal of Mathematical Physics 44 (2003), no. 9, 4157-4175.
10. P. J. Forrester, N. E. Frankel, T. M. Garoni, and N. S. Witte, Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable bosons, Communications in Mathematical Physics 238 (2003), no. 1-2, 257-285.
11. P. J. Forrester and E. M. Rains, Interrelationships between orthogonal, unitary and symplectic matrix ensembles, Random Matrix Models and Their Applications (P. M. Bleher and A. R. Its, eds.), Mathematical Sciences Research Institute Publications, vol. 40, Cambridge University Press, Cambridge, 2001, pp. 171-207.
12. _, Interpretations of some parameter dependent generalizations of classical matrix ensembles, Probability Theory and Related Fields 131 (2005), no. 1, 1-61.
13. W. B. Gragg, Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle, Journal of Computational and Applied Mathematics 46 (1993), no. 1-2, 183-198.
14. J. Gunson, Proof of a conjecture by Dyson in the statistical theory of energy levels, Journal of Mathematical Physics 3 (1962), no. 4, 752-753.
15. J. P. Keating and N. C. Snaith, Random matrix theory and ζ(1/2+it), Communications in Mathematical Physics 214 (2000), no. 1, 57-89.
16. _, Random matrix theory and L-functions at s = 1/2, Communications in Mathematical Physics 214 (2000), no. 1, 91-110.
17. R. Killip and I. Nenciu, Matrix models for circular ensembles, International Mathematics Research Notices 2004 (2004), no. 50, 2665-2701.
18. M. L. Mehta and F. J. Dyson, Statistical theory of the energy levels of complex systems. V, Journal of Mathematical Physics 4 (1963), no. 5, 713-719.
19. Yu. A. Neretin, Rayleigh triangles and nonmatrix interpolation of matrix beta integrals, Sbronik: Mathematics 194 (2003), no. 3-4, 515-540 (Russian).
20. E. M. Rains, Increasing subsequences and the classical groups, Electronic Journal of Combinatorics 5 (1998), R12, 9.
21. J. H. Wilkinson, The evaluation of the zeros of ill-conditioned polynomials, I, Numerische Mathematik 1 (1959), no. 1, 150-166.
22. N. S. Witte and P. J. Forrester, Gap probabilities in the finite and scaled Cauchy random matrix ensembles, Nonlinearity 13 (2000), no. 6, 1965-1986.