Cluster-cluster correlations and constraints on the correlation hierarchy

Details Cluster-cluster correlations and constraints on the correlation hierarchy Cluster-cluster correlations and constraints on the correlation hierarchy

Aug 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988apj...331..641h&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 331, Aug. 15, 1988, p. 641-647.

Statistics

Computation

16

Computational Astrophysics, Cosmology, Fractals, Galactic Clusters, Statistical Correlation, Constraints, Hierarchies, Normal Density Functions, Random Walk, Trees (Mathematics)

Scientific paper

The hypothesis that galaxies cluster around clusters at least as strongly as they cluster around galaxies imposes constraints on the hierarchy of correlation amplitudes, QN ≥ N!21-NN2-N, in hierarchical clustering models. The distributions which saturate these constraints are the Rayleigh-Lévy random walk fractals proposed by Mandelbrot; for these fractal distributions cluster-cluster correlations are all identically equal to galaxy-galaxy correlations. If correlation amplitudes exceed the constraints, as is observed, then cluster-cluster correlations must exceed galaxy-galaxy correlations, as is observed.

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