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The ability to tailor the spectral response of photonic devices is paramountto the advancement of a broad range of applications. The vast design spaceoffered by disordered optical media provide enhanced functionality for spectraltailoring, although it is challenging to map the spectral properties of suchcomplex systems to their structural attributes. In this work, we investigatecorrelations between the statistics underlying the structure of random arraysof particles and their spectral properties. We consider 1D and 2D arrays ofdielectric nanorods suspended in vacuum and numerically study their opticalscattering properties in the visible wavelength range. We show that thescattering cross section of a random particle array is primarily governed byits configuration statistics and is independent of its exact instantiation orthe number of its constituent particles. We further exploit the strongcorrelations between the statistics and spectral properties of random particlearrays to predict their spectral response. By using a semi-analytical nearestneighbor coupling model, we produce accurate qualitative estimates of thespectral responses of both one and two-dimensional random arrays for differentconfiguration statistics. The results presented in this manuscript will opennew avenues for optimizing large-scale random systems to achieve enhancedoptical functionalities for a wide variety of applications.

Statistics dependent spectral properties of random arrays of particles