Limit laws for products of free and independent random variables

Hari Bercovici; Vittorino Pata

Studia Mathematica (2000)

  • Volume: 141, Issue: 1, page 43-52
  • ISSN: 0039-3223

Abstract

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We determine the distributional behavior of products of free (in the sense of Voiculescu) identically distributed random variables. Analogies and differences with the classical theory of independent random variables are then discussed.

How to cite

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Bercovici, Hari, and Pata, Vittorino. "Limit laws for products of free and independent random variables." Studia Mathematica 141.1 (2000): 43-52. <http://eudml.org/doc/216772>.

@article{Bercovici2000,
abstract = {We determine the distributional behavior of products of free (in the sense of Voiculescu) identically distributed random variables. Analogies and differences with the classical theory of independent random variables are then discussed.},
author = {Bercovici, Hari, Pata, Vittorino},
journal = {Studia Mathematica},
keywords = {noncommutative probability theory; free multiplication; free independence; products of positive random variables; convolutions},
language = {eng},
number = {1},
pages = {43-52},
title = {Limit laws for products of free and independent random variables},
url = {http://eudml.org/doc/216772},
volume = {141},
year = {2000},
}

TY - JOUR
AU - Bercovici, Hari
AU - Pata, Vittorino
TI - Limit laws for products of free and independent random variables
JO - Studia Mathematica
PY - 2000
VL - 141
IS - 1
SP - 43
EP - 52
AB - We determine the distributional behavior of products of free (in the sense of Voiculescu) identically distributed random variables. Analogies and differences with the classical theory of independent random variables are then discussed.
LA - eng
KW - noncommutative probability theory; free multiplication; free independence; products of positive random variables; convolutions
UR - http://eudml.org/doc/216772
ER -

References

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  1. [1] H. Bercovici and V. Pata, Classical versus free domains of attraction, Math. Res. Lett. 2 (1995), 791-795. Zbl0846.60023
  2. [2] H. Bercovici and V. Pata, Stable laws and domains of attraction in free probability theory, with an appendix by P. Biane, Ann. of Math. 149 (1999), 1023-1060. Zbl0945.46046
  3. [3] H. Bercovici and V. Pata, Functions of regular variation and freely stable laws, Ann. Mat. Pura Appl., to appear. Zbl1072.46044
  4. [4] H. Bercovici and D. Voiculescu, Lévy-Hinčin type theorems for multiplicative and additive free convolution, Pacific J. Math. 153 (1992), 217-248. Zbl0769.60013
  5. [5] H. Bercovici and D. Voiculescu, Free convolution of measures with unbounded support, Indiana Univ. Math. J. 42 (1993), 733-773. Zbl0806.46070
  6. [6] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, MA, 1954. Zbl0056.36001
  7. [7] B. V. Gnedenko and A. N. Kolmogorov, Multiplication of certain non-commuting random variables, J. Operator Theory 18 (1987), 223-235. 
  8. [8] D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, CRM Monogr. Ser. 1, Amer. Math. Soc., Providence, RI, 1992. 

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