Distribution for nonsymmetric V-monotone position operators

TL;DR

This paper analyzes the vacuum distribution of nonsymmetric V-monotone position operators, deriving its exact form and illustrating it with computer-generated graphs for various parameters.

Contribution

It provides the first explicit determination of the distribution for a family of nonsymmetric V-monotone position operators, including its atomic and continuous parts.

Findings

Distribution has a unique atom and an absolutely continuous part.

Exact form of the distribution is derived using the Cauchy--Stieltjes transform.

Graphs illustrate the distribution's behavior for different parameter values.

Abstract

We investigate the vacuum distribution of a family of partial sums of nonsymmetric position operators, depending on a real parameter $\lambda$, and acting on the discrete Fock space in the framework of V-monotone independence. We analyze the combinatorics of the moments of this distribution, and using its Cauchy--Stieltjes transform, we determine its exact form, consisting of a unique atom and an absolutely continuous part. Finally, we present computer-generated graphs that illustrate the distribution for several values of the intensity parameter $\lambda$.