Cluster size diversity, percolation, and complex systems

Diversity of cluster size has been used as a measurement of complexity in s everal systems that generate a statistical distribution of clusters. Using Monte Carlo simulations, we present a statistical analysis of the cluster s ize diversity and the number of clusters generated on randomly occupied lat tices for the Euclidean dimensions 1 to 6. A tuning effect for diversity of cluster size and critical probabilities associated with the maximum divers ity and the maximum number of clusters are reported. The probability of max imum diversity is related to the percolation threshold and several scaling relations between the variables measured are reported. The statistics of cl uster size diversity has important consequences in the statistical descript ion of the Universe as a complex system. [S1063-651X(99)08709-7].