Limit theorems in free probability theory II

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1. [1] Akhiezer N.I., The classical moment problem and some related questions in analysis, Hafner, New York, 1965 Zbl0135.33803
2. [2] Akhiezer N.I., Glazman I.M., Theory of Linear Operators in Hilbert Space, Ungar, New York, 1963 
3. [3] Barndorff-Nielsen O.E., Thorbjørnsen S., Selfdecomposability and Levy processes in free probability, Bernoulli, 2002, 8, 323–366 Zbl1024.60022
4. [4] Belinschi S.T., Complex analysis methods on noncommutative probability, preprint available at http://arxlv.org/abs/math/0603104v1 
5. [5] Belinschi S.T., Bercovici H., Hincin’s theorem for multiplicative free convolutions, Canad. Math. Bull., to appear Zbl1144.46056
6. [6] Bercovici H., Voiculescu D., Lévy-Hinčin type theorems for multiplicative and additive free convolution, Pacific J. Math., 1992, 153, 217–248 Zbl0769.60013
7. [7] Bercovici H., Voiculescu D., Free convolution of measures with unbounded support, Indiana Univ. Math. J., 1993, 42, 733–773 http://dx.doi.org/10.1512/iumj.1993.42.42033 Zbl0806.46070
8. [8] Bercovici H., Pata V, Stable laws and domains of attraction in free probability theory, Ann. of Math., 1999, 149, 1023–1060 http://dx.doi.org/10.2307/121080 Zbl0945.46046
9. [9] Bercovici H., Pata V, Limit laws for products of free and independent random variables, Studia Math., 2000, 141, 43–52 Zbl0968.46051
10. [10] Bercovici H., Wang J.C., Limit theorems for free multiplicative convolutions, preprint available at http://arxlv.org/abs/math/0612278v1 Zbl1166.46039
11. [11] Biane Ph., Processes with free increments, Math. Z., 1998, 227, 143–174 http://dx.doi.org/10.1007/PL00004363 Zbl0902.60060
12. [12] Chistyakov C.P., Cötze F., The arithmetic of distributions in free probability theory, preprint available at http://arxlv.org/abs/math/0508245v1 
13. [13] Chistyakov G.P., Götze F., Limit theorems in free probability theory I, Ann. Probab., 2008, 36, 54–90 http://dx.doi.org/10.1214/009117907000000051 Zbl1157.46037
14. [14] Gnedenko B.V., Kolmogorov A.N., Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, 1968 
15. [15] Hiai F., Petz D., The Semicircle Law, Free Random Variables and Entropy, A.M.S., Providence, Rl, 2000 Zbl0955.46037
16. [16] Loéve M., Probability theory, VNR, New York, 1963 
17. [17] Parthasarathy K.R., Probability measures on metric spaces, Academic Press, New York and London, 1967 Zbl0153.19101
18. [18] Sazonov V.V., Tutubalin V.N., Probability distributions on topological groups, Theory Probab. Appl., 1966, 11, 1–45 http://dx.doi.org/10.1137/1111001 Zbl0171.38701
19. [19] Voiculescu D.V, Multiplication of certain noncommutlng random variavles, J. Operator Theory, 1987, 18, 223–235 
20. [20] Voiculesku D., Dykema K., Nica A., Free random variables, CRM Monograph Series, No 1, A.M.S., Providence, Rl, 1992 
21. [21] Voiculescu D.V., The analogues of entropy and Fisher’s information mesure in free probability theory I, Comm. Math. Phys., 1993, 155, 71–92 http://dx.doi.org/10.1007/BF02100050 Zbl0781.60006
22. [22] Voiculescu D.V., The coalgebra of the free difference quotient and free probability, Int. Math. Res. Not., 2000, 2, 79–106 http://dx.doi.org/10.1155/S1073792800000064 Zbl0952.46038
23. [23] Voiculescu D.V., Analytic subordination consequences of free Markovianity, Indiana Univ. Math. J., 2002, 51, 1161–1166 http://dx.doi.org/10.1512/iumj.2002.51.2252 Zbl1040.46044

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