Powers of large random unitary matrices and toeplitz determinants

Transactions of the American Mathematical Society

Volumn 362, Issue 3, 2010, Pages 1169-1187

  Duits, Maurice ^a,c   Johansson, Kurt ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77950870965     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-09-04542-5     Document Type: Article

References (14)

1. Basor, E., Widom, H., On a Toeplitz determinant identity of Borodin and Okounkov, Integral Equations Operator Theory, 2000, 37(4), 397-401. MR1780119 (2001g:47042b)
2. Basor, E., Widom, H., Toeplitz and Wiener-Hopf determinants with piecewise continuous symbols, J. Funct. Anal., 1983, 3, 387-413. MR695420 (85d:47026)
3. Borodin, A., Okounkov, A., A Fredholm determinant formula for Toeplitz determinants, Integral Equations Operator Theory, 2000, 37(4), 386-396. MR1780118 (2001g:47042a)
4. Böttcher, A., Silbermann, B., Introduction to large truncated Toeplitz matrices, Springer- Verlag, New York, 1999. MR1724795 (2001b:47043)
5. Diaconis, P., Patterns in eigenvalues: The 70th Josiah Willard Gibbs Lecture, Bull. Amer. Math. Soc., 2003, 40(2), 155-178. MR1962294 (2004d:15017) (Pubitemid 36507738)
6. Diaconis, P., Evans, S., Linear functionals of eigenvalues of random matrices, Trans. Amer. Math. Soc., 2001, 353, 2615-2633. MR1828463 (2002d:60003) (Pubitemid 33766703)
7. Diaconis, P., Shahshahani, M., On the eigenvalues of random matrices, In Studies in Applied Probability. J. Appl. Probab.: Special Vol. 31A, 1994, 49-62. MR1274717 (95m:60011) (Pubitemid 126040789)
8. Geronimo, J. S., Case, K. M., Scattering theory and polynomials orthogonal on the unit circle, J. Math. Phys., 1979, 20(2), 299-310. MR519213 (80f:81100)
9. Hughes, C. P., Rudnick, Z., Linear statistics of low-lying zeros of L-functions, Quart. J. Math., 2003, 54(3), 309-333. MR2013141 (2005a:11131) (Pubitemid 37446081)
10. Hughes, C. P., Rudnick, Z., Mock Gaussian behavior for linear statistics of classical compact groups, J. Phys. A, 2003, 36(2), 2919-2932. MR1986399 (2004e:60012) (Pubitemid 36508512)
11. Rains, E., High powers of random elements of compact Lie groups, Probab. Theory Related Fields, 1997, 107, 219-241. MR1431220 (98b:15026) (Pubitemid 127372687)
12. Soshnikov, A., The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities, Ann. Prob., 2000, 28, 1353-1370. MR1797877 (2002f:15035) (Pubitemid 33212835)
13. Widom, H., Asymptotic behavior of block Toeplitz matrices and determinants, II, Adv. in Math., 1976, 21 (1), 1-29. MR0409512 (53:13266b)
14. Wieand, K., Eigenvalue distributions of random unitary matrices, Probab. Theory Related Fields, 2002, 123(2), 202-224. MR1900322 (2003b:60016)