Convolution and limit theorems for conditionally free random variables

Pacific Journal of Mathematics

Volumn 175, Issue 2, 1996, Pages 357-388

  Bozejko, Marek ^a   Leinert, Michael ^b   Speicher, Roland ^b  

^a UNIVERSITY OF WROC AW   (Poland)

^b UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000683126     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1996.175.357     Document Type: Article

References (27)

1. N.I. Achieser and I.M. Glasmann, Theorie der linearen Operatoren im Hubert Raum, Akademie-Verlag, Berlin, 1960.
2. P. Biane, Some properties of crossings and partitions, 1994, preprint.
3. M. Bożejko, Positive definite functions on the free group and the non commutative Riesz product, Boll. Un. Mat. Ital., 5A (1986), 13-21.
4. _, Uniformly bounded representations of free groups, J. Reine Angew. Math., 377 (1987), 170-186.
5. M. Bożejko and R. Speicher, ψ-independent and symmetrized white noises Quantum Probability and Related Topics, (L. Accardi, ed.), World Scientific, Singapore, VI (1991), 219-236.
6. T. Cabanal-Duvillard, Variation quantique sur l'independance: La σ-independance, 1993, preprint.
7. P.H. Edelman, Chain Enumeration and Non-Crossing Partitions, Discr. Math., 31 (1980), 171-180.
8. _, Multichains, Non-Crossing Partitions and Trees, Discr. Math., 40 (1982), 171-179.
9. W.L. Girko, Random Matrices, Kiev, 1975, (Russian).
10. U. Haagerup, An Example of a Non Nuclear C*-Algebra which has the Metric Approximation Property, Invent. Math., 50 (1979), 279-293.
11. P. Hilton and J. Pederson, Catalan Numbers, Their Generalization, and Their Uses, Math. Intelligencer, 13(2) (1991), 64-75.
12. G. Kreweras, Sur les partitions non croisees d'un cycle, Discr. Math., 1 (1972), 333-350.
13. H. Maassen, Addition of freely independent random variables, J. Funct. Anal., 106 (1992), 409-438.
14. A. Nica, Crossings and embracings of set-partitions and q-analogues of the logarithm of the Fourier transform, Discr. Math., to appear.
15. P. Neu and R. Speicher, A self-consistent master equation and a new kind of cumulants, Z. Phys. B, 92 (1993), 399-407.
16. _, Non-linear master equation and non-crossing cumulants, Quantum Probability and Related Topics, (L. Accardi, ed.), World Scientific, Singapore, IX (1994), 311-326.
17. Y. Poupard, Etude et denombrement paralleles des partitions non croisees d'un cycle et coupage d'un polygone convexe, Discr. Math., 2 (1972), 279-288.
18. R. Simion, Combinatorial statistics on non-crossing partitions, 1991, preprint.
19. R. Simion and D. Ullman, On the structure of the lattice of non-crossing partitions, Discr. Math., 98 (1991), 193-206.
20. R. Speicher, A New Example of "Independence" and "White Noise", Probab. Th. Rel. Fields, 84 (1990), 141-159.
21. _, Multiplicative functions on the lattice of non-crossing partitions and free convolution, Math. Ann., 298 (1994), 611-628.
22. R. Speicher and R. Woroudi, Boolean convolution, The Fields Institute Communications, to appear.
23. D. Voiculescu, Symmetries of some reduced free product C*-algebras, Operator Algebras and their Connection with Topology and Ergodic Theory, Lecture Notes in Mathematics, Springer, Heidelberg, 1132 (1985), 556-588.
24. _, Addition of certain non-commuting random variables, J. Funct. Anal., 66 (1986), 323-346.
25. D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, AMS, 1992.
26. W. von Waldenfels, An approach to the theory of pressure broadening of spectral lines, Lecture Notes in Mathematics, Springer, Heidelberg, 296 (1973), 19-69.
27. R. Woroudi, Boolesche Faltung, Heidelberg, diploma thesis, 1993.