Commutators of free random variables
Alexandru Nica and Roland Speicher
Source: Duke Math. J. Volume 92, Number 3
(1998), 553-592.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077231677
Mathematical Reviews number (MathSciNet): MR1620518
Zentralblatt MATH identifier: 0968.46053
Digital Object Identifier: doi:10.1215/S0012-7094-98-09216-X
References
[1] N. I. Akhiezer, The classical moment problem and some related questions in analysis, Translated by N. Kemmer, Hafner Publishing Co., New York, 1965.
Mathematical Reviews (MathSciNet): MR32:1518
Zentralblatt MATH: 0135.33803
[2] G. E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976.
Mathematical Reviews (MathSciNet): MR58:27738
Zentralblatt MATH: 0371.10001
[3] H. Bercovici and D. Voiculescu, Free convolution of measures with unbounded support, Indiana Univ. Math. J. 42 (1993), no. 3, 733–773.
Mathematical Reviews (MathSciNet): MR95c:46109
Zentralblatt MATH: 0806.46070
Digital Object Identifier: doi:10.1512/iumj.1993.42.42033
[4] H. Bercovici and D. Voiculescu, Regularity questions for free convolution, preprint, 1996.
Mathematical Reviews (MathSciNet): MR1639647
Zentralblatt MATH: 0927.46048
[5] Ph. Biane, Processes with free increments, to appear in Math. Z.
Mathematical Reviews (MathSciNet): MR1605393
Digital Object Identifier: doi:10.1007/PL00004363
[6] Ph. Biane, The density of free stable distributions, preprint, 1996.
[7] G. Kreweras, Sur les partitions non croisées d'un cycle, Discrete Math. 1 (1972), no. 4, 333–350.
Mathematical Reviews (MathSciNet): MR46:8852
Zentralblatt MATH: 0231.05014
Digital Object Identifier: doi:10.1016/0012-365X(72)90041-6
[8] A. Nica, $R$-transforms of free joint distributions and non-crossing partitions, J. Funct. Anal. 135 (1996), no. 2, 271–296.
Mathematical Reviews (MathSciNet): MR96k:46119
Zentralblatt MATH: 0837.60008
Digital Object Identifier: doi:10.1006/jfan.1996.0011
[9] A. Nica, $R$-diagonal pairs arising as free off-diagonal compression, Indiana Univ. Math. J. 45 (1996), no. 2, 529–544.
Mathematical Reviews (MathSciNet): MR97j:46069
Zentralblatt MATH: 0879.46031
Digital Object Identifier: doi:10.1512/iumj.1996.45.1280
[10] A. Nica and R. Speicher, A “Fourier transform” for multiplicative functions on non-crossing partitions, J. Algebraic Combin. 6 (1997), no. 2, 141–160.
Mathematical Reviews (MathSciNet): MR98i:46070
Zentralblatt MATH: 0872.06005
Digital Object Identifier: doi:10.1023/A:1008643104945
[11] A. Nica and R. Speicher, On the multiplication of free $N$-tuples of noncommutative random variables, Amer. J. Math. 118 (1996), no. 4, 799–837, with an appendix “Alternative proofs for the type $H$ free Poisson variables and for the free compression results” by D. Voiculescu.
Mathematical Reviews (MathSciNet): MR98i:46069
Zentralblatt MATH: 0872.06005
Digital Object Identifier: doi:10.1353/ajm.1996.0034
[12] A. Nica and R. Speicher, $R$-diagonal pairs—a common approach to Haar unitaries and circular elements, Free probability theory (Waterloo, ON, 1995), Fields Inst. Commun., vol. 12, Amer. Math. Soc., Providence, RI, 1997, pp. 149–188.
Mathematical Reviews (MathSciNet): MR98b:46083
Zentralblatt MATH: 0889.46053
[13] R. Speicher, Multiplicative functions on the lattice of noncrossing partitions and free convolution, Math. Ann. 298 (1994), no. 4, 611–628.
Mathematical Reviews (MathSciNet): MR95h:05012
Zentralblatt MATH: 0791.06010
Digital Object Identifier: doi:10.1007/BF01459754
[14] D. Voiculescu, Symmetries of some reduced free product $C\sp \ast$-algebras, Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983), Lecture Notes in Math., vol. 1132, Springer, Berlin, 1985, pp. 556–588.
Mathematical Reviews (MathSciNet): MR87d:46075
Zentralblatt MATH: 0618.46048
Digital Object Identifier: doi:10.1007/BFb0074909
[15] D. Voiculescu, Addition of certain noncommuting random variables, J. Funct. Anal. 66 (1986), no. 3, 323–346.
Mathematical Reviews (MathSciNet): MR87j:46122
Zentralblatt MATH: 0651.46063
Digital Object Identifier: doi:10.1016/0022-1236(86)90062-5
[16] D. Voiculescu, Multiplication of certain noncommuting random variables, J. Operator Theory 18 (1987), no. 2, 223–235.
Mathematical Reviews (MathSciNet): MR89b:46076
Zentralblatt MATH: 0662.46069
[17] D. Voiculescu, Free probability theory: random matrices and von Neumann algebras, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, pp. 227–241.
Mathematical Reviews (MathSciNet): MR97f:46102
Zentralblatt MATH: 0839.46059
[18] D. Voiculescu, K. Dykema, and A. Nica, Free random variables, CRM Monograph Series, vol. 1, American Mathematical Society, Providence, RI, 1992.
Mathematical Reviews (MathSciNet): MR94c:46133
Zentralblatt MATH: 0795.46049
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