Mathematics – Probability
Scientific paper
Aug 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989a%26a...220....1b&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 220, no. 1-2, Aug. 1989, p. 1-29.
Mathematics
Probability
183
Cosmology, Galactic Clusters, Mass Distribution, Statistical Distributions, Universe, Luminosity, Probability Distribution Functions, Scaling Laws, Statistical Correlation, Voids
Scientific paper
The galaxy count or matter content within a randomly placed cell is determined under the assumption of scale-invariance of the many-body correlation function. The probability of finding N objects at a given volume is found to decrease exponentially with N at small scales and to behave as a power law with an upper, and possibly a lower, exponential cut-off at larger scales. It is demonstrated that the large-scale void probability is a scale-free extrapolation of its small-scale behavior, and that as long as the correlation functions are power laws, this void distribution is not compatible with the linear theory. It is noted that counts in cells are approximately Gaussian at large scales, provided that the density fluctuations are less than 10 percent of the mean.
Balian Roger
Schaeffer Richard
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