Second order freeness and fluctuations of random matrices: II. Unitary random matrices

Advances in Mathematics

Volumn 209, Issue 1, 2007, Pages 212-240

  Mingo, James A ^a   Śniady, Piotr ^b   Speicher, Roland ^a  

^a QUEEN S UNIVERSITY   (Canada)

^b UNIVERSITY OF WROC AW   (Poland)

Author keywords

Free probability; Haar distributed unitary random matrices; Second order freeness

Indexed keywords

EID: 33750960799     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2006.05.003     Document Type: Article

References (21)

1. Ambjørn J., Jurkiewicz J., and Makeenko Y. Multiloop correlators for two-dimensional quantum gravity. Phys. Lett. B 251 (1990) 517-524
2. Biane P. Some properties of crossings and partitions. Discrete Math. 175 1-3 (1997) 41-53
3. Collins B. Moments and cumulants of polynomial random variables of unitary groups, the Itzykson-Zuber integral, and free probability. IMRN 17 (2003) 953-982
4. Collins B., and Śniady P. Integration with respect to the Haar measure on unitary, orthogonal and symplectic group. Comm. Math. Phys. 264 (2006) 773-795
5. Diaconis P. Patterns in eigenvalues: The 70th Josiah Willlard Gibbs lecture. Bull. Amer. Math. Soc. 40 (2003) 155-178
6. Diaconis P., and Shahshahani M. On the eigenvalues of random matrices. J. Appl. Probab. A 31 (1994) 49-62
7. Johansson K. On fluctuations of eigenvalues of random hermitian matrices. Duke Math. J. 91 (1998) 151-204
8. T. Kusalik, J. Mingo, R. Speicher, Orthogonal polynomials and fluctuations of random matrices, J. Reine Angew. Math., in press
9. Lehner F. Cumulants in noncommutative probability I, Noncommutative exchangeability systems. Math. Z. 248 (2004) 67-100
10. Mingo J., and Nica A. Annular non-crossing permutations and partitions, and second-order asymptotics for random matrices. IMRN 28 (2004) 1413-1460
11. Mingo J., and Speicher R. Second order freeness and fluctuations of random matrices: I. Gaussian and Wishart matrices and cyclic Fock spaces. J. Funct. Anal. 235 (2006) 226-270
12. A. Nica, R. Speicher, Lectures on the Combinatorics of Free Probability Theory, Paris, 1999
13. Hiai F., and Petz D. The Semicircle Law, Free Random Variables and Entropy (2000), Amer. Math. Soc., Providence, RI
14. Politzer D. Random-matrix description of the distribution of mesoscopic conductance. Phys. Rev. B 40 (1989) 11917-11919
15. Rǎdulescu F. Combinatorial aspects of Connes's embedding conjecture. preprint (2004). math.OA/0404308
16. Voiculescu D. Limit laws for random matrices and free products. Invent. Math. 104 (1991) 201-220
17. Voiculescu D. A strengthened asymptotic freeness result for random matrices with applications to free entropy. IMRN 1 (1998) 41-63
18. Voiculescu D. Lectures on free probability theory. Lecture Notes in Math. vol. 1738 (2000), Springer 279-349
19. Voiculescu D., Dykema K., and Nica A. Free Random Variables (1992), Amer. Math. Soc., Providence, RI
20. Weingarten D. Asymptotic behavior of group integrals in the limit of infinite rank. J. Math. Phys. 19 (1978) 999-1001
21. Xu F. A random matrix model from two-dimensional Yang-Mills theory. Comm. Math. Phys. 190 (1997) 287-307