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

top
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

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.