# On some generalization of the t-transformation

Banach Center Publications (2010)

- Volume: 89, Issue: 1, page 165-187
- ISSN: 0137-6934

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topAnna Dorota Krystek. "On some generalization of the t-transformation." Banach Center Publications 89.1 (2010): 165-187. <http://eudml.org/doc/282200>.

@article{AnnaDorotaKrystek2010,

abstract = {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 two parameters and is different from the Poisson measures for (a,b)-deformation. We also show that the -deformed free convolution is different from the convolution obtained as the deformed conditionally free convolution of Bożejko, Leinert and Speicher. Thus the does not satisfy the Bożejko property.},

author = {Anna Dorota Krystek},

journal = {Banach Center Publications},

keywords = {free convolution; conditionally free convolution; deformation; limit theorems; moment cumulant formulae},

language = {eng},

number = {1},

pages = {165-187},

title = {On some generalization of the t-transformation},

url = {http://eudml.org/doc/282200},

volume = {89},

year = {2010},

}

TY - JOUR

AU - Anna Dorota Krystek

TI - On some generalization of the t-transformation

JO - Banach Center Publications

PY - 2010

VL - 89

IS - 1

SP - 165

EP - 187

AB - 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 two parameters and is different from the Poisson measures for (a,b)-deformation. We also show that the -deformed free convolution is different from the convolution obtained as the deformed conditionally free convolution of Bożejko, Leinert and Speicher. Thus the does not satisfy the Bożejko property.

LA - eng

KW - free convolution; conditionally free convolution; deformation; limit theorems; moment cumulant formulae

UR - http://eudml.org/doc/282200

ER -

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