Explorations into the mean nearest-neighbor distance in uniform and unimodal random distributions

The two-dimensional mean nearest neighbor distance and other distance distribution metrics, in uniform and unimodal normal distributions of random sequential addition hard disc computer-generated patterns, have been studied. First, more instances have been recorded in sufficient number to provide for more averaging and higher resolution data. Second, a facile, surprisingly accurate, method for estimating mean nearest neighbor distance in 2D uniform random distributions is presented. Third, the change in mean nearest neighbor distance as a function of the area fraction and standard deviation of the normal distribution of the disc diameter is discussed. It has been found that, while the changes are small (on the order of a few percent) both positive and negative deviations are observed. Consequences for higher dimension problems and multi-modal distributions are discussed.

Automated summary

This study investigates the two-dimensional mean nearest neighbor distance and other distance distribution metrics in uniform and unimodal normal distributions of random sequential addition hard disc computer-generated patterns. An accurate method for estimating the mean nearest neighbor distance is proposed and the changes in distance are discussed. The findings have implications for higher dimension problems and multi-modal distributions.