Displaying similar documents to “A note on regularity for free convolutions”

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...

Almost sure absolute continuity of Bernoulli convolutions

Michael Björklund, Daniel Schnellmann (2010)

Annales de l'I.H.P. Probabilités et statistiques

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We prove an extension of a result by Peres and Solomyak on almost sure absolute continuity in a class of symmetric Bernoulli convolutions.