We discuss the mean and variance of the number ‘point-particles’ inside a disk D R centered at the origin of the complex plane and of radius R > 0 with respect to an infinite true polyanalytic process of index by quantizing the phase space via a set of generalized coherent states (CSs) of the harmonic oscillator on . By this procedure, the spectrum of the quantum observable representing the indicator function ofD R (viewed as a classical observable) allows to compute the mean value of . The variance of is obtained as a special eigenvalue of a quantum observable involving the auto-convolution of . By adopting a CSs quantization approach, we seek to identify classical observables on whose quantum counterparts may encode the first cumulants of through spectral properties.