The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution

Łukasz Jan Wojakowski

Banach Center Publications (2007)

  • Volume: 78, Issue: 1, page 309-314
  • ISSN: 0137-6934

Abstract

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We study deformations of the free convolution arising via invertible transformations of probability measures on the real line T:μ ↦ Tμ. We define new associative convolutions of measures by μ ⊞ T ν = T - 1 ( T μ ⊞ T ν ) . We discuss infinite divisibility with respect to these convolutions, and we establish a Lévy-Khintchine formula. We conclude the paper by proving that for any such deformation of free probability all probability measures μ have the Nica-Speicher property, that is, one can find their convolution power μ ⊞ T s for all s ≥ 1. This behaviour is similar to the free case, as in the original paper of Nica and Speicher [NS].

How to cite

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Łukasz Jan Wojakowski. "The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution." Banach Center Publications 78.1 (2007): 309-314. <http://eudml.org/doc/282110>.

@article{ŁukaszJanWojakowski2007,
abstract = {We study deformations of the free convolution arising via invertible transformations of probability measures on the real line T:μ ↦ Tμ. We define new associative convolutions of measures by $μ ⊞_T ν = T^\{-1\}(Tμ ⊞ Tν)$. We discuss infinite divisibility with respect to these convolutions, and we establish a Lévy-Khintchine formula. We conclude the paper by proving that for any such deformation of free probability all probability measures μ have the Nica-Speicher property, that is, one can find their convolution power $μ^\{⊞_\{T\}s\}$ for all s ≥ 1. This behaviour is similar to the free case, as in the original paper of Nica and Speicher [NS].},
author = {Łukasz Jan Wojakowski},
journal = {Banach Center Publications},
keywords = {free convolution; deformations; Lévy-Khintchine formula; Nica-Speicher property},
language = {eng},
number = {1},
pages = {309-314},
title = {The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution},
url = {http://eudml.org/doc/282110},
volume = {78},
year = {2007},
}

TY - JOUR
AU - Łukasz Jan Wojakowski
TI - The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution
JO - Banach Center Publications
PY - 2007
VL - 78
IS - 1
SP - 309
EP - 314
AB - We study deformations of the free convolution arising via invertible transformations of probability measures on the real line T:μ ↦ Tμ. We define new associative convolutions of measures by $μ ⊞_T ν = T^{-1}(Tμ ⊞ Tν)$. We discuss infinite divisibility with respect to these convolutions, and we establish a Lévy-Khintchine formula. We conclude the paper by proving that for any such deformation of free probability all probability measures μ have the Nica-Speicher property, that is, one can find their convolution power $μ^{⊞_{T}s}$ for all s ≥ 1. This behaviour is similar to the free case, as in the original paper of Nica and Speicher [NS].
LA - eng
KW - free convolution; deformations; Lévy-Khintchine formula; Nica-Speicher property
UR - http://eudml.org/doc/282110
ER -

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