Affiliation:
1. Department of Mathematics , College of Science and Arts in Gurayat , [ 125894]Jouf University, Gurayat , Saudi Arabia
Abstract
Abstract
In this paper, we deal with the notion of
V
a
{V_{a}}
-deformed free convolution, introduced in [A. D. Krystek and L. J. Wojakowski,
Associative convolutions arising from conditionally free convolution,
Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 2005, 3, 515–545], from a point of view related to the theory of Cauchy–Stieltjes kernel (CSK) families and their corresponding variance functions. We determine the formula for variance function under a power of
V
a
{V_{a}}
-deformed free convolution. Then we provide an approximation of elements of the CSK family generated by
V
a
{V_{a}}
-deformed free Poisson distribution.