Second order freeness and fluctuations of random matrices: I. Gaussian and Wishart matrices and cyclic Fock spaces

Journal of Functional Analysis

Volumn 235, Issue 1, 2006, Pages 226-270

  Mingo, James A ^a   Speicher, Roland ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

Free probability; Random matrices; Second order freeness

Indexed keywords

EID: 33645944056     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.10.007     Document Type: Article

References (22)

1. Ambjorn J., Jurkiewicz J., and Makeenko Y. Multiloop correlators for two-dimensional quantum gravity. Phys. Lett. B 251 (1990) 517-524
2. Anshelevich M. Appell polynomials and their relatives. Int. Math. Res. Not. 65 (2004) 3469-3531
3. Cabanal-Duvillard T. Fluctuations de la loi empirique de grandes matrices aleatoires. Ann. Inst. H. Poincaré Probab. Statist. 37 (2001) 373-402
4. Capitaine M., and Casalis M. Asymptotic freeness by generalized moments for Gaussian and Wishart matrices. Application to beta matrices. Indiana Univ. Math. J. 53 (2004) 397-431
5. Eynard B. Random matrices, cours de physique theorique de Saclay (2000). http://www-spht.cea.fr/articles/t01/014
6. Glockner P., Schürmann M., and Speicher R. Realization of free white noises. Arch. Math. 58 (1992) 407-416
7. Graczyk P., Letac G., and Massam H. The complex Wishart distribution and the symmetric group. Ann. Statist. 31 (2003) 287-309
8. 2 ) ) is not a group. Ann. of Math. 162 (2005) 711-775
9. Hiai F., and Petz D. The Semicircle Law, Free Random Variables and Entropy (2000), Amer. Math. Soc., Providence, RI
10. Janson S. Gaussian Hilbert Spaces. Cambridge Tracts in Math. vol. 129 (1997), Cambridge Univ. Press, Cambridge
11. Johansson K. On fluctuations of eigenvalues of random Hermitian matrices. Duke Math. J. 91 (1998) 151-204
12. Kusalik T., Mingo J., and Speicher R. Orthogonal polynomials and fluctuations of random matrices. preprint. math.OA/0503169
13. Mingo J., and Nica A. Annular non-crossing permutations and partitions, and second-order asymptotics for random matrices. Int. Math. Res. Not. 28 (2004) 1413-1460
14. Mingo J., Śniady P., and Speicher R. Second order freeness and fluctuations of random matrices: II. Unitary random matrices. preprint. math.OA/0405258
15. A. Nica, R. Speicher, Lectures on the Combinatorics of Free Probability Theory, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, in press
16. Politzer H.D. Random matrix description of the distribution of mesoscopic conductance. Phys. Rev. B 40 (1989) 11917-11919
17. Speicher R. A new example of "Independence" and "White Noise". Probab. Theory Related Fields 84 (1990) 141-159
18. Speicher R. Combinatorial theory of the free product with amalgamation and operator-valued free probability theory. Mem. Amer. Math. Soc. 132 627 (1998)
19. Voiculescu D. Limit laws for random matrices and free products. Invent. Math. 104 (1991) 201-220
20. Voiculescu D. Lectures on free probability theory. Lecture Notes in Math. vol. 1738 (2000), Springer, Berlin 279-349
21. Voiculescu D., Dykema K., and Nica A. Free Probability Theory (1991), Amer. Math. Soc., Providence, RI
22. Zvonkin A. Matrix integrals and map enumeration: an accessible introduction. Math. Comput. Modelling 26 (1997) 281-304