A non-commutative Lévy-Cramér continuity theorem

作者: Yan Pautrat , Vojkan Jaksic , Claude-Alain Pillet

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摘要: In classical probability, the Levy-Cramer continuity theorem is a standard tool for proving convergence in distribution of family random variables. We prove non-commutative analogues this result.

参考文章(26)
Dénes Petz, An invitation to the algebra of canonical commutation relations Leuven University Press. ,(1990)
Barry Simon, Michael Reed, Methods of Modern Mathematical Physics ,(1972)
Paul André Meyer, Quantum Probability for Probabilists ,(1993)
Hans Maassen, Quantum probability applied to the damped harmonic oscillator arXiv: Quantum Physics. ,(2004)
Greg Kuperberg, A tracial quantum central limit theorem Transactions of the American Mathematical Society. ,vol. 357, pp. 459- 471 ,(2003) , 10.1090/S0002-9947-03-03449-4
L. Accardi, A. Frigerio, Y. G. Lu, The weak coupling limit as a quantum functional central limit Communications in Mathematical Physics. ,vol. 131, pp. 537- 570 ,(1990) , 10.1007/BF02098275
Stéphane Attal, Yan Pautrat, From Repeated to Continuous Quantum Interactions Annales Henri Poincaré. ,vol. 7, pp. 59- 104 ,(2006) , 10.1007/S00023-005-0242-8
Stéphane Attal, Alain Joye, The Langevin equation for a quantum heat bath Journal of Functional Analysis. ,vol. 247, pp. 253- 288 ,(2007) , 10.1016/J.JFA.2006.09.019
N. Giri, W. Waldenfels, An algebraic version of the central limit theorem Probability Theory and Related Fields. ,vol. 42, pp. 129- 134 ,(1978) , 10.1007/BF00536048