Spatial Statistics and Information Geometry for Parametric Statistical Models of Galaxy Clustering

Poisson spatial processes of points and ofextended objects representing smoothed clusters ofgalaxies are considered; some results are obtained forplanar representations of random filaments, which may help interpret the findings of the Las CampanasRedshift Survey. Based on a model for the voidprobability function, a family of gamma-relateddistributions is investigated as a three-dimensionalmodel for the clustering of galaxies. The unclusteredmodels in this family correspond to the random case andto maximum information-theoretic entropy. The Riemannianinformation metric and Gaussian curvature are derived for the parameter space of thefamily of models, which provides a background on whichto write dynamics for cluster evolution.