The Cosmological Mass Distribution from Cayley Trees with Disorder
Abstract
We present a new approach to the statistics of the cosmic density field and to the mass distribution of bound structures, based on the formalism of Cayley trees. Our approach includes in one random process both fluctuations and interactions of the density perturbations. We connect treerelated quantities, like the partition function or its generating function, to the mass distribution. The Press & Schechter mass function and the Smoluchowski kinetic equation are naturally recovered as two limiting cases, corresponding to independent Gaussian fluctuations and to aggregation of highcontrast condensations, respectively. Numerical realizations of the complete random process on the tree yield an excess of largemass objects relative to the Press & Schechter function. When interactions are fully effective, a powerlaw distribution with logarithmic slope  2 is generated.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1994
 DOI:
 10.1086/174833
 arXiv:
 arXiv:astroph/9411017
 Bibcode:
 1994ApJ...435..528C
 Keywords:

 Cosmology;
 Galactic Clusters;
 Galaxies;
 Kinetic Equations;
 Density Wave Model;
 Energetic Particles;
 Equations Of Motion;
 Mathematical Models;
 Astrophysics;
 COSMOLOGY: LARGESCALE STRUCTURE OF UNIVERSE;
 COSMOLOGY: THEORY;
 GALAXIES: CLUSTERING;
 GALAXIES: FORMATION;
 METHODS: NUMERICAL;
 Astrophysics
 EPrint:
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