# 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

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topBercovici, 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

top- [1] H. Bercovici and V. Pata, Classical versus free domains of attraction, Math. Res. Lett. 2 (1995), 791-795. Zbl0846.60023
- [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] H. Bercovici and V. Pata, Functions of regular variation and freely stable laws, Ann. Mat. Pura Appl., to appear. Zbl1072.46044
- [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] H. Bercovici and D. Voiculescu, Free convolution of measures with unbounded support, Indiana Univ. Math. J. 42 (1993), 733-773. Zbl0806.46070
- [6] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, MA, 1954. Zbl0056.36001
- [7] B. V. Gnedenko and A. N. Kolmogorov, Multiplication of certain non-commuting random variables, J. Operator Theory 18 (1987), 223-235.
- [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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