Displaying similar documents to “Remarks on t-transformations of measures and 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.

On Q-independence, limit theorems and q-Gaussian distribution

Marcin Marciniak (1998)

Studia Mathematica

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We formulate the notion of Q-independence which generalizes the classical independence of random variables and free independence introduced by Voiculescu. Here Q stands for a family of polynomials indexed by tiny partitions of finite sets. The analogs of the central limit theorem and Poisson limit theorem are proved. Moreover, it is shown that in some special cases this kind of independence leads to the q-probability theory of Bożejko and Speicher.

Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case

Michael M. Erlihson, Boris L. Granovsky (2008)

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

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We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ∼ , →∞, >0, where is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations...

On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions

Florent Benaych-Georges (2010)

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

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In this paper, we prove a result linking the square and the rectangular -transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko–Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.