Displaying similar documents to “Limit theorems in free probability theory II”

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...

Convolution of radius functions on ℝ³

Konstanty Holly (1994)

Annales Polonici Mathematici

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We reduce the convolution of radius functions to that of 1-variable functions. Then we present formulas for computing convolutions of an abstract radius function on ℝ³ with various integral kernels - given by elementary or discontinuous functions. We also prove a theorem on the asymptotic behaviour of a convolution at infinity. Lastly, we deduce some estimates which enable us to find the asymptotics of the velocity and pressure of a fluid (described by the Navier-Stokes equations) in...

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...

Poisson perturbations

Andrew D. Barbour, Aihua Xia (1999)

ESAIM: Probability and Statistics

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