Displaying similar documents to “New Examples of Convolutions and Non-Commutative Central Limit Theorems”

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.

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...