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Banach Center Publications

2010 | 89 | 1 | 165-187

On some generalization of the t-transformation

EN

Abstrakty

EN
Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation $U^{𝕋}$ 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 𝕋-deformed free convolutions is still a Kesten measure, but the Poisson limit depends on the two parameters and is different from the Poisson measures for (a,b)-deformation. We also show that the 𝕋-deformed free convolution is different from the convolution obtained as the deformed conditionally free convolution of Bożejko, Leinert and Speicher. Thus the 𝕋 does not satisfy the Bożejko property.

165-187

wydano
2010

Twórcy

autor
• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland