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Interpolations between bosonic and fermionic relations given by generalized brownian motions

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References

  1. L. Accardi, F. Fagnola, and J. Quaegebeur, A representation free quantum stochastic calculus,J. Funct. Anal. 104 (1992), 149–197.

    Article  MATH  MathSciNet  Google Scholar 

  2. D.B. Applebaum and R.L. Hudson, Fermion Ito’s formula and stochastic evolutions,Comm. Math. Phys 96 (1984), 473–496.

    Article  MATH  MathSciNet  Google Scholar 

  3. H. Bervovici and D. Voiculescu, Free Convolution of Measures with Unbounded Support,Indiana Univ. Math. J. 42 (1993), 733–773.

    Article  MathSciNet  Google Scholar 

  4. N. Bourbaki,Groupes et algebres de lie, Chap. 4,5,6, Hermann 1968.

  5. M. Bożejko, M. Leinert and R. Speicher, Convolution and limit theorems for conditionally free random variables,Proc. J. Math (to appear)

  6. M. Bożejko and R. Speicher, An Example of Generalized Brownian Motion,Comm. Math. Phys. 137 (1991), 519–531.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Bożejko and R. Speicher, An example of a generalized Brownian motion II, inQuantum Probability and Related Topics VII, World Scientific, Singapore 1992, 67–77.

    Google Scholar 

  8. M. Bożejko and R. Speicher, ψ-Independent and Symmetrized White Noises, inQuantum Probability and Related Topics VI, World Scientific, Singapore 1991, 219–236.

    Google Scholar 

  9. M. Bożejko, Positive definite functions on the free group and the non commutative Riesz product,Boll. Un. Math. Ital. 5A (1986), 13–22.

    Google Scholar 

  10. D.E. Evans, OnO n ,Publ. RIMS 16 (1980), 915–927.

    Article  MATH  Google Scholar 

  11. D. Fivel, Interpolation between Fermi and Bose statistics using generalized commutators,Phys. Rev. Lett. 65 (1990), 3361–3364.

    Article  MathSciNet  Google Scholar 

  12. N. Giri and W. von Waldenfels, An algebraic version of the central limit theorem,Z. Wahrscheinlichkeitstheorie verw. Gebiete 42 (1978), 129–134.

    Article  MATH  Google Scholar 

  13. O.W. Greenberg, Particles with small violations of Fermi or Bose statistics,Phys. Rev. D 43 (1991), 4111–4120.

    Article  MathSciNet  Google Scholar 

  14. R.L. Hudson and K.R. Parthasarathy, Quantum Ito’s formula and stochastic evolution,Comm. Math. Phys 93 (1984), 301–323.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Kreweras, Sur les partitions non croisees d’un cycle,Discr. Math. 1 (1972), 333–350.

    Article  MATH  MathSciNet  Google Scholar 

  16. B. Kümmerer, Markov dilations onW*-algebras,J. Funct. Anal. 63 (1985), 139–177.

    Article  MATH  MathSciNet  Google Scholar 

  17. B. Kümmerer, Markov dilations and non-commutative Poisson processes, preprint.

  18. B. Kümmerer and J. Prin, Generalized white noise and non-commutative stochastic integration, preprint.

  19. B. Kümmerer and R. Speicher, Stochastic Integration on the Cuntz Algebra ,J. Funct. Anal. 103 (1992), 372–408.

    Article  MATH  MathSciNet  Google Scholar 

  20. R. Lenczewski and K. Podgorski, Aq-Analog of the Quantum Central Limit Theorem forSU q (2),J. Math. Phys. 33 (1992), 2768–2778.

    Article  MATH  MathSciNet  Google Scholar 

  21. H. Maassen, Addition of Freely Independent Random Variables,J. Funct. Anal. 106 (1992), 409–438.

    Article  MATH  MathSciNet  Google Scholar 

  22. P. Neu and R. Speicher, A self-consistent master equation and a new kind of cumulants,Z. Phys. B 92 (1993), 399–407.

    Article  MathSciNet  Google Scholar 

  23. K.R. Parthasarathy,An introduction to quantum stochastic calculus, Birkhäuser 1992.

  24. K.R. Parthasarathy and K. Schmidt,Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory, Springer-Verlag (LNM 272), Heidelberg 1972.

    MATH  Google Scholar 

  25. R. Speicher, A New Example of ‘Independence’ and ‘White Noise’,Probab. Th. Rel. Fields 84 (1990), 141–159.

    Article  MATH  MathSciNet  Google Scholar 

  26. R. Speicher, A non-commutative central limit theorem,Math. Z. 209 (1992), 55–66.

    Article  MATH  MathSciNet  Google Scholar 

  27. R. Speicher, Generalized Statistics of Macroscopic Fields,Lett. Math. Phys. 27 (1993), 97–104.

    Article  MATH  MathSciNet  Google Scholar 

  28. R. Speicher, Multiplicative functions on the lattice of non-crossing partitions and free convolution,Math. Ann. 298 (1994), 611–628

    Article  MATH  MathSciNet  Google Scholar 

  29. D. Voiculescu, Symmetries of some reduced free productC*-algebras, inOperator Algebras and their Connection with Topology and Ergodic Theory, LNM 1132, Springer, Heidelberg 1985, 556–588.

    Google Scholar 

  30. D. Voiculescu, Addition of certain non-commuting random variables,J. Funct. Anal. 66 (1986), 323–346.

    Article  MATH  MathSciNet  Google Scholar 

  31. W. von Waldenfels, An algebraic central limit theorem in the anti-commuting case,Z. Wahrscheinlichkeitstheorie verw.Gebiete 42 (1978), 135–140.

    Article  MATH  Google Scholar 

  32. D. Zagier, Realizability of a Model in Infinite Statistics,Comm. Math. Phys. 147 (1992), 199–210.

    Article  MATH  MathSciNet  Google Scholar 

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Bożejko, M., Speicher, R. Interpolations between bosonic and fermionic relations given by generalized brownian motions. Math Z 222, 135–160 (1996). https://doi.org/10.1007/BF02621861

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