Voronoï cell-size distribution and Edwards' compactivity of the parking lot model

We find by Monte Carlo simulations that the distribution of Voronoï cell sizes for the parking lot model follows a gamma distribution with shape parameter k approximately 2 for high enough packing fractions varphi . A gamma distribution of Voronoï cells sizes was found recently by Aste [Europhys. Lett. 79, 24003 (2007)] in experiments of static packings of monodisperse spheres. This statistic implies that, for high varphi , Edwards' compactivity of the parking lot model depends linearly on the average volume per cell, as predicted by the statistical mechanics calculation of Tarjus and Viot, which explicitly counted the blocked configurations of this model [Phys. Rev. E 69, 011307 (2004)].