arXiv subjects

Adrian Dacko

Publications and source records attributed to Adrian Dacko.

3 recordsLinked to original sources

arXiv2026

Distribution for nonsymmetric V-monotone position operators

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 $\lambda$.

math.FA↗

arXiv2023

Central limit measure for V-monotone independence

We study the central limit distribution $\mu$ for V-monotone independence. Using its Cauchy--Stieltjes transform, we prove that $\mu$ is absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}$ and we give its density $\rho$ in an implicit form. We present a computer generated graph of $\rho$.

math.FA↗

arXiv2019

V-monotone independence

We introduce and study a new notion of non-commutative independence, called V-monotone independence, which can be viewed as an extension of the monotone independence of Muraki. We investigate the combinatorics of mixed moments of V-monotone random variables and prove the central limit theorem. We obtain a combinatorial formula for the limit moments and we find the solution of the differential equation for the moment generating function in the implicit form.

math.FA↗