Analytical results for size-topology correlations in 2D disk and cellular packings

Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a unimodal distribution of both areas and number of neighbors. Empirically, strong correlations between these distributions have been observed and formulated as universal laws. Using only the local, correlation-free granocentric model approach with no free parameters, we construct accurate analytical descriptions for disk crystallization, size-topology correlations, and Lemaître's law.