Multinomial identities arising from free probality theory

Journal of Combinatorial Theory. Series A

Volumn 101, Issue 1, 2003, Pages 1-19

  Śniady, Piotr ^a  

^a UNIVERSITY OF WROC AW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037275821     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0097-3165(02)00006-7     Document Type: Article

References (18)

1. P. Biane, Representations of symmetric groups and free probability, Adv. Math. 138 (1) (1998) 126-181.
2. M. Bozejko, M. Leinert, R. Speicher, Convolution and limit theorems for conditionally free random variables, Pacific J. Math. 175 (2) (1996) 357-388.
3. K. Dykema, U. Haagerup, Decomposability of Voiculescu's circular operator and DT-operators, preprint, 2001.
4. K. Dykema, C. Yan, Generating functions for moments of the quasi-nilpotent DT operator, preprint, 2001.
5. ω , preprint, 2001.
6. R.V. Kadison, J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. I, Reprint of the 1983 original, American Mathematical Society, Providence, RI, 1997.
7. R.V. Kadison, J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. II, American Mathematical Society, Providence, RI, 1997 (Advanced theory, Corrected reprint of the 1986 original).
8. G. Kreweras, Sur les partitions non croisées d'un cycle, Discrete Math. 1 (4) (1972) 333-350.
9. G.N. Raney, Functional composition patterns and power series reversion, Trans. Amer. Math. Soc. 94 (1960) 441-451.
10. D. Shlyakhtenko, Randon Gaussian band matrices and freeness with amalgamation, Internat. Math. Res. Notices (20) (1996) 1013-1025.
11. D. Shlyakhtenko, Gaussian random band matrices and operator-valued free probability theory, in: Quantum Probability (Gdańsk, 1997), (Robert Alicki, Marek Bozejko, Władysław Majewski, Eds.), Polish Academy of Science, Warsaw, 1998, pp. 359-368.
12. R. Speicher, Free probability theory and non-crossing partitions, Sém. Lothar. Combin., 39: Art. B39c (electronic), 1997, 38pp.
13. R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Mem. Amer. Math. Soc. 132 (627) (1998) x + 88.
14. R. Speicher, P. Neu, Physical applications of freeness, in: XIIth International Congress of Mathematical Physics (ICMP '97) (Brisbane), International Press, Cambridge, MA, 1999, pp. 261-266.
15. D. Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1) (1991) 201-220.
16. D. Voiculescu, Free probability theory: random matrices and von Neumann algebras, in: Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, pp. 227-241.
17. D. Voiculescu, Lectures on free probability theory, in: Lectures on Probability Theory and Statistics (Saint-Flour, 1998), Springer, Berlin, 2000, pp. 279-349.
18. D.V. Voiculescu, K.J. Dykema, A. Nica, Free Random Variables, A Noncommutative Probability Approach to Free Products with Applications to Random Matrices, Operator Algebras and Harmonic Analysis on Free Groups, American Mathematical Society, Providence, RI, 1992.