New limit theorems related to Fermi convolution

Abstract

This paper is a continuation of study of Fermi convolution from the perspective of Cauchy-Stieltjes Kernel (CSK) families. By the use of variance function machinery, we prove some new limit theorems related to Fermi convolution. We give an approximation of elements of the CSK family generated by the Fermi Gaussian distribution. We also provide a new limit theorem related to Fermi convolution and involving free multiplicative convolution.