Displaying similar documents to “The arithmetic of distributions in free probability theory”

Limit theorems in free probability theory II

Gennadii Chistyakov, Friedrich Götze (2008)

Open Mathematics

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Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle 𝕋 we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.

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.

The L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures

Przemysław Liszka (2014)

Open Mathematics

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Very recently bounds for the L q spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and...