Summary: This paper contains not only a review of the author [Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8, No. 3, 505–514 (2005; Zbl 1087.46020); Colloq. Math. 109, No. 1, 101–106 (2007; Zbl 1121.46026)] but also new results. Let \(\mu\) be a probability measure on \(\mathbb C\) derived from the complex moment problem associated with the Jacobi-Szegő parameter. First, we show that \(\widetilde \mu\) has a rotation invariance property. It means that a one-mode interacting Fock space can be realized as a Hilbert space of analytic \(L^2\)-functions with respect to a rotation invariant measure on \(\mathbb C\). As typical examples, the Gaussian and Bessel kernel measures on \(\mathbb C\) are presented. Secondly, the relationship among the golden ratio, Bessel kernel measure and classical random variables is discussed. Furthermore, the distribution of the Lévy’s stochastic area is also treated. In the end, we give a short remark on the binomial distribution.
For the entire collection see [Zbl 1165.81004].