Year: 2025
Type: article
Abstract: This study is devoted to the detailed examination of the concept of (a,b)-deformation, defined for parameters a∈R and b>0. The analysis is conducted within the framework of Cauchy–Stieltjes kernel (CSK) families of probability measures, with particular attention given to the role of their variance functions (VFs). Using the VF as the main analytical tool, it is shown that the (a,b)-deformation of any measure belonging to the free Meixner family (FMF) remains within the same family. Moreover, the VF framework provides a powerful and flexible means for establishing new limit theorems associated with (a,b)-deformed free convolution. In particular, several novel limiting behaviors are derived, which naturally encompass both free and Boolean additive convolutions as special cases.
Source: Symmetry
DOI: 10.3390/sym17111954
Institutions: Jouf University, Princess Nourah bint Abdulrahman University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Award: G7183163005
OpenAlex ID: W4416395756