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

• Autorzy: Łukasz Jan Wojakowski
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 46L53: Noncommutative probability and statistics
• 46L54: Free probability and free operator algebras
• 60E10: Characteristic functions; other transforms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 309-314

Daty

wydano

2007

Twórcy

autor

Łukasz Jan Wojakowski

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

Identyfikatory

DOI

10.4064/bc78-0-23