Pacific Journal of Mathematics

Convolution and limit theorems for conditionally free random variables.

Marek Bożejko, Michael Leinert, and Roland Speicher

Article information

Source
Pacific J. Math., Volume 175, Number 2 (1996), 357-388.

Dates
First available in Project Euclid: 6 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102353149

Mathematical Reviews number (MathSciNet)
MR1432836

Zentralblatt MATH identifier
0874.60010

Subjects
Primary: 46L50
Secondary: 46K99: None of the above, but in this section 46N50: Applications in quantum physics 81S25: Quantum stochastic calculus

Citation

Bożejko, Marek; Leinert, Michael; Speicher, Roland. Convolution and limit theorems for conditionally free random variables. Pacific J. Math. 175 (1996), no. 2, 357--388. https://projecteuclid.org/euclid.pjm/1102353149


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References

  • [AG1] N.I.Achieser and I.M.Glasmann, Theorie der linearen Operatoren im Hubert Raum, Akademie-Verlag, Berlin, 1960.
  • [Bia] P. Biane, Some properties of crossings and partitions, 1994, preprint.
  • [Bozl] M. Bozejko, Positive definite functions on the free group and the non commutative Riesz product,Boll. Un. Mat. Ital., 5A (1986), 13-21.
  • [Boz2] M. Bozejko, Uniformly bounded representationsof free groups,J. Reine Angew. Math., 377 (1987), 170-186.
  • [BSp] M. Bozejko and R. Speicher, -independent and symmetrized white noisesQuantum Probability and Related Topics, (L. Accardi, ed.), World Scientific, Singapore, VI (1991), 219-236.
  • [CDu] T. Cabanal-Duvillard, Variationquantiquesur Vindependance: La -independance, 1993, preprint.
  • [Edel] P.H. Edelman, Chain Enumeration and Non-CrossingPartitions, Discr. Math., 31 (1980), 171-180.
  • [Ede2] P.H. Edelman, Multichains, Non-CrossingPartitions and Trees,Discr. Math., 40 (1982), 171-179.
  • [Gir] W.L. Girko, Random Matrices,Kiev, 1975, (Russian).
  • [Haa] U. Haagerup, An Example of a Non Nuclear C*-Algebra which has the Metric Ap- proximation Property,Invent. Math., 50 (1979), 279-293.
  • [HiP] P. Hilton and J. Pederson, CatalanNumbers, Their Generalization, and Their Uses, Math. Intelligencer, 13(2) (1991), 64-75.
  • [Kre] G. Kreweras, Sur les partitions non croisees d'un cycle, Discr. Math., 1 (1972), 333-350.
  • [Maa] H. Maassen, Addition of freely independent random variables,J. Funct. Anal., 106 (1992), 409-438.
  • [Nic] A. Nica, Crossingsand embracingsof set-partitionsand q-analogues of thelogarithm of the Fourier transform, Discr. Math., to appear.
  • [NSpl] P. Neu and R. Speicher, A self-consistentmaster equationand a new kind of cumu- lants, Z. Phys. B, 92 (1993), 399-407.
  • [NSp2] P. Neu and R. Speicher, Non-linear master equationand non-crossingcumulants, Quantum Proba- bility and Related Topics, (L. Accardi, ed.), World Scientific, Singapore, IX (1994), 311-326.
  • [Pou] Y. Poupard, Etude et denombrementparallelesdes partitions non croiseesd'un cycle et coupage d'un polygone convexe,Discr. Math., 2 (1972), 279-288.
  • [Sim] R. Simion, Combinatorialstatistics on non-crossing partitions, 1991, preprint.
  • [SiU] R. Simion and D. Ullman, On the structure of the lattice of non-crossing partitions, Discr. Math., 98 (1991), 193-206.
  • [Spel] R. Speicher, A New Example of "Independence" and "White Noise", Probab. Th. Rel. Fields, 84 (1990), 141-159.
  • [Spe2] R. Speicher, Multiplicativefunctions on the lattice of non-crossingpartitions and free convolution,Math. Ann., 298 (1994), 611-628.
  • [SpW] R. Speicher and R. Woroudi, Booleanconvolution,The Fields Institute Communi- cations, to appear.
  • [Voil] D.Voiculescu, Symmetries ofsome reducedfree product C*-algebras, OperatorAl- gebras andtheir Connection with Topology andErgodic Theory, Lecture Notes in Mathematics, Springer, Heidelberg, 1132 (1985), 556-588.
  • [Voi2] D.Voiculescu, Addition ofcertain non-commuting random variables, J. Funct. Anal., 66 (1986), 323-346.
  • [VDN] D.Voiculescu, K.Dykema andA.Nica, Free Random Variables, AMS, 1992.
  • [vWa] W.vonWaldenfels, An approach to thetheory ofpressure broadening ofspectral lines, Lecture Notes in Mathematics, Springer, Heidelberg, 296(1973), 19-69.
  • [Wor] R.Woroudi, Boolesche Faltung, Heidelberg, diploma thesis, 1993.