Remarks on t-transformations of measures and convolutions
Marek Bożejko, Janusz Wysoczański (2001)
Annales de l'I.H.P. Probabilités et statistiques
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Marek Bożejko, Janusz Wysoczański (2001)
Annales de l'I.H.P. Probabilités et statistiques
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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.
Colin C. Graham (1975)
Colloquium Mathematicae
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K. Urbanik (1964)
Studia Mathematica
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Mlotkowski, Wojciech (2010)
Documenta Mathematica
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Serban Teodor Belinschi (2006)
Annales de l'I.H.P. Probabilités et statistiques
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M. Rajagopalan (1963)
Colloquium Mathematicae
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K. Urbanik (1973)
Studia Mathematica
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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 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...