Recent Applications of Voronoi Tesselation and Analysis of Their Size Distributions with the Generalized Wigner Surmise

While Voronoi tessellation has long been applied in spatial studies, analysis of their cell-size distribution using the single-adjustable-parameter generalized Wigner surmise, P_β(s) = as^βexp(-bs², has only been done in the last decade. Here we discuss some intriguing examples: Mitko et al. (2019) consider the evolution of morphology during growth of island films of low-e dielectric films via vapor deposition polymerization. Löbl et al. (2019) probe infilling Al-droplet-etched nanoholes in an AlGaAs surface. In both cases, estimates of the critical nucleus size were extracted from the value of the exponenet β determined from a fit to P_β(s). We discuss the results and their implications. In other tantalizing examples, the Voronoi cell-size was not [yet] analyzed using P_β(s). Brookes (2017) uses Voronoi analysis of cells on the outer layer of eye-banked corneas to assess their viability before transplanting. Konishi et al. (2017) studied the growth-rate dependence of the spatial distribution of self-assembled 2D quantum dots on InAs-GaAs. They also consider the influence of modest array size.