ClusterCluster Correlations and Constraints on the Correlation Hierarchy
Abstract
The hypothesis that galaxies cluster around clusters at least as strongly as they cluster around galaxies imposes constraints on the hierarchy of correlation amplitudes, Q_N_ >= N!2^1N^N^2N^, in hierarchical clustering models. The distributions which saturate these constraints are the RayleighLevy random walk fractals proposed by Mandelbrot; for these fractal distributions clustercluster correlations are all identically equal to galaxygalaxy correlations. If correlation amplitudes exceed the constraints, as is observed, then clustercluster correlations must exceed galaxygalaxy correlations, as is observed.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1988
 DOI:
 10.1086/166587
 Bibcode:
 1988ApJ...331..641H
 Keywords:

 Computational Astrophysics;
 Cosmology;
 Fractals;
 Galactic Clusters;
 Statistical Correlation;
 Constraints;
 Hierarchies;
 Normal Density Functions;
 Random Walk;
 Trees (Mathematics);
 Astrophysics;
 COSMOLOGY;
 GALAXIES: CLUSTERING