Displaying similar documents to “On asymptotic growth of the support of free multiplicative convolutions.”

A remark on p-convolution

Rafał Sałapata (2011)

Banach Center Publications

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We introduce a p-product of algebraic probability spaces, which is the definition of independence that is natural for the model of noncommutative Brownian motions, described in [10] (for q = 1). Using methods of the conditionally free probability (cf. [4, 5]), we define a related p-convolution of probability measures on ℝ and study its relations with the notion of subordination (cf. [1, 8, 9, 13]).

New Examples of Convolutions and Non-Commutative Central Limit Theorems

Marek Bożejko, Janusz Wysoczański (1998)

Banach Center Publications

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A family of transformations on the set of all probability measures on the real line is introduced, which makes it possible to define new examples of convolutions. The associated central limit theorems are studied, and examples of the limit measures, related to the classical, free and boolean convolutions, are shown.

The arithmetic of distributions in free probability theory

Gennadii Chistyakov, Friedrich Götze (2011)

Open Mathematics

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We give an analytical approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and Schur functions. We consider the set of probability distributions as a semigroup M equipped with the operation of free convolution and prove a Khintchine type theorem for the factorization of elements of this semigroup. An element of M contains either indecomposable (“prime”) factors or it belongs to a class, say I 0, of distributions without...

On some generalization of the t-transformation

Anna Dorota Krystek (2010)

Banach Center Publications

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Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation U of probability measures on the real line ℝ, which is another possible generalization of the t-transformation. Using that deformation we define a new convolution by deformation of the free convolution. The central limit measure with respect to the -deformed free convolutions is still a Kesten measure, but the Poisson limit depends on the...

Limit Measures Related to the Conditionally Free Convolution

Melanie Hinz, Wojciech Młotkowski (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We describe the limit measures for some class of deformations of the free convolution, introduced by A. D. Krystek and Ł. J. Wojakowski. In particular, we provide a counterexample to a conjecture from their paper.

Limit laws for products of free and independent random variables

Hari Bercovici, Vittorino Pata (2000)

Studia Mathematica

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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.