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

Banach Center Publications (2007)

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

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topŁukasz 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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