ArticleOriginal scientific text

Title

Limit laws for products of free and independent random variables

Authors 1, 2

Affiliations

  1. Mathematics Department, Indiana University, Bloomington, IN 47405, U.S.A.
  2. Dipartimento di Matematica, Università di Brescia, 25123 Brescia, Italy

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.

Bibliography

  1. H. Bercovici and V. Pata, Classical versus free domains of attraction, Math. Res. Lett. 2 (1995), 791-795.
  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.
  3. H. Bercovici and V. Pata, Functions of regular variation and freely stable laws, Ann. Mat. Pura Appl., to appear.
  4. H. Bercovici and D. Voiculescu, Lévy-Hinčin type theorems for multiplicative and additive free convolution, Pacific J. Math. 153 (1992), 217-248.
  5. H. Bercovici and D. Voiculescu, Free convolution of measures with unbounded support, Indiana Univ. Math. J. 42 (1993), 733-773.
  6. B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, MA, 1954.
  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.
Pages:
43-52
Main language of publication
English
Accepted
2000-04-10
Published
2000
Exact and natural sciences