  We discuss the mean and variance of the number \textquotedblleft
point-particles\textquotedblright\ $\sharp _{D_{R}}$\ inside a disk $D_{R}$
centered at the origin of the complex plane $\mathbb{C}$ and of radius $R>0$
with respect to a Ginibre-type (polyanalytic) process of index $m\in
\mathbb{Z}_{+}$ by quantizing the phase space $\mathbb{C} $ via a set of
generalized coherent states $\left\vert z,m\right\rangle $ of the harmonic
oscillator on $L^{2}\left(\mathbb{R}\right) $. By this procedure, the spectrum
of the quantum observable representing the indicator function $\chi _{D_{R}}$
of $ D_{R}$ (viewed as a classical observable) allows to compute the mean value
of $\sharp _{D_{R}}$. The variance of $\sharp _{D_{R}}$ is obtained as a
special eigenvalue of a quantum observable involving to the auto-convolution of
$\chi _{D_{R}}.$ By adopting a coherent states quantization approach, we seek
to identify classical observables on $\mathbb{C},$ whose quantum counterparts
may encode the first cumulants of $\sharp _{D_{R}}$ through spectral
properties.
