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The interpolation between the classical and monotone independence given by the twisted CCR

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present an interpolation between the classically independent Gaussian random variables and an anti-monotone independent family of semicircle elements given by the twisted CCR.
Rocznik
Tom
Strony
63--69
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
  • Faculty of Cybernetics, Kiev Taras Shevchenko National University, Kiev, Ukraine
autor
  • Faculty of Cybernetics, Kiev Taras Shevchenko National University, Kiev, Ukraine
Bibliografia
  • [1] Accardi L., Bożejko M.: Interacting Fock spaces and Gaussinization of probability measures. Infin. Dim. Anal., Quant. Prob. and Rel. Topics, 1, No. 4 (1998), 663-670
  • [2] Bratelli O., Robinson D. W.: Operator algebras and quantum statistical mechanics. Berlin, Heidelberg, New York, Springer Verlag 1981
  • [3] Biedenharn L.C.: The quantum group SUq(2) and q-analogue of the boson operators. J. Phys.A., 22 (1989), L873-L878
  • [4] Bożejko M., Kummerer B., Speicher R.: q-Gaussian processes: non-commutative and classical aspects. Commun. Math. Phys., 185 (1997) 129-154
  • [5] Bożejko M., Speicher R.: An example of a generalized Brownian motion. Comm. Math. Phys., 137 (1991), pp. 519-531
  • [6] Bożejko M., Speicher R.: An example of a generalized Brownian motion II, Infin. Dim. Anal., Quant. Prob. and Rel. Topics, 7 (1992), pp 97-120
  • [7] Franz U.: Monotone independence is associative. Infin. Dim. Anal. Quant. Prob. and Rel. Topics, 4, No. 3 (2001), pp. 401-407
  • [8] Macfarlane A. J.: On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q. J. Phys. A., 22 (1989), 4581-4588
  • [9] Meyer P.-A.: Quantum probability for probabilists. LNM, vol. 1538, Berlin, Springer Verlag 1995
  • [10] Muraki N.: Monotonic independence, monotonic central limit theorem and monotonic law of small numbers. Infin. Dim. Anal., Quant. Prob. and Rel. Topics, 4, No. 1 (2001), pp. 39-58
  • [11] Pusz W., Woronowicz S.L.: Twisted second quantization. Reports Math. Phys., 27 (1989), 251-263
  • [12] Proskurin D., Samoilenko Yu.: Stability of the C* -algebra associated with the twisted CCR. Algebras and Rep. Theory, 5 (2002), 433-444
  • [13] Speicher R., von Waldenfels W.: A general central limit theorem and invariance principle. Quant. Prob. and Rel. Topics, 9, pp. 371-387
  • [14] Voiculescu D., Dykema K., Nica A.: Free Random Variables, CRM book series, 1992
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0005-0087
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