Lévy type characterization of stable laws for free random variables
HTML articles powered by AMS MathViewer
- by Vittorino Pata PDF
- Trans. Amer. Math. Soc. 347 (1995), 2457-2472 Request permission
Abstract:
We give a description of stable probability measures relative to free additive convolution. The definition of domain of attraction is given, and a proof is provided of the noncommutative analogue of Lévy Theorem.References
- Hari Bercovici and Dan Voiculescu, Free convolution of measures with unbounded support, Indiana Univ. Math. J. 42 (1993), no. 3, 733–773. MR 1254116, DOI 10.1512/iumj.1993.42.42033 H. Bercovici and V. Pata, The law of large numbers for free identically distributed variables, Preprint, 1995.
- Hari Bercovici and Dan Voiculescu, Lévy-Hinčin type theorems for multiplicative and additive free convolution, Pacific J. Math. 153 (1992), no. 2, 217–248. MR 1151559, DOI 10.2140/pjm.1992.153.217
- William Feller, An introduction to probability theory and its applications. Vol. II. , 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0270403
- I. A. Ibragimov and Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971. With a supplementary chapter by I. A. Ibragimov and V. V. Petrov; Translation from the Russian edited by J. F. C. Kingman. MR 0322926 J.M. Lindsay and V. Pata, Some weak laws of large numbers in non-commutative probability, Preprint, 1994.
- Hans Maassen, Addition of freely independent random variables, J. Funct. Anal. 106 (1992), no. 2, 409–438. MR 1165862, DOI 10.1016/0022-1236(92)90055-N
- F. J. Murray and J. Von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), no. 1, 116–229. MR 1503275, DOI 10.2307/1968693
- Dan Voiculescu, Addition of certain noncommuting random variables, J. Funct. Anal. 66 (1986), no. 3, 323–346. MR 839105, DOI 10.1016/0022-1236(86)90062-5
- Dan Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991), no. 1, 201–220. MR 1094052, DOI 10.1007/BF01245072
- D. V. Voiculescu, K. J. Dykema, and A. Nica, Free random variables, CRM Monograph Series, vol. 1, American Mathematical Society, Providence, RI, 1992. A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. MR 1217253, DOI 10.1090/crmm/001
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 2457-2472
- MSC: Primary 46L50; Secondary 60E07
- DOI: https://doi.org/10.1090/S0002-9947-1995-1311913-3
- MathSciNet review: 1311913