  The ability to tailor the spectral response of photonic devices is paramount
to the advancement of a broad range of applications. The vast design space
offered by disordered optical media provide enhanced functionality for spectral
tailoring, although it is challenging to map the spectral properties of such
complex systems to their structural attributes. In this work, we investigate
correlations between the statistics underlying the structure of random arrays
of particles and their spectral properties. We consider 1D and 2D arrays of
dielectric nanorods suspended in vacuum and numerically study their optical
scattering properties in the visible wavelength range. We show that the
scattering cross section of a random particle array is primarily governed by
its configuration statistics and is independent of its exact instantiation or
the number of its constituent particles. We further exploit the strong
correlations between the statistics and spectral properties of random particle
arrays to predict their spectral response. By using a semi-analytical nearest
neighbor coupling model, we produce accurate qualitative estimates of the
spectral responses of both one and two-dimensional random arrays for different
configuration statistics. The results presented in this manuscript will open
new avenues for optimizing large-scale random systems to achieve enhanced
optical functionalities for a wide variety of applications.
