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• # Artykuł - szczegóły

## Banach Center Publications

2007 | 78 | 1 | 309-314

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

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].

309-314

wydano
2007

### Twórcy

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