Distribution for nonsymmetric V-monotone position operators

We investigate the vacuum distribution of a family of partial sums of nonsymmetric position operators with a real parameter $\lambda$, acting on the discrete Fock space in the setting of $V$-monotone independence. We study the combinatorics of the moments of this distribution, and we use its Cauchy–Stieltjes transform to obtain its exact form – the unique atom and its remaining, absolutely continuous part. We present computer-generated graphs for several values of the intensity $\lambda$. This is joint work with Lahcen Oussi.