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Author Saslaw, W. C.
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ♦ GALAXY CLUSTERS ♦ DISTRIBUTION FUNCTIONS ♦ ASTROPHYSICS ♦ GRAVITATION ♦ KOLMOGOROV EQUATION ♦ MANY-BODY PROBLEM ♦ STOCHASTIC PROCESSES ♦ THERMODYNAMICS ♦ DIFFERENTIAL EQUATIONS ♦ EQUATIONS ♦ FUNCTIONS ♦ Astrophysics & Cosmology- Galaxies
Abstract Some of the mathematical and physical properties of the probability distribution f(N) which describes the observed clustering of galaxies are derived, including an exact, explicit formula for the generating function of f(N). This shows that different volumes are stochastically independent and that the form of the function applies to its two-dimensional projection on the sky as well as in three dimensions. Two different cluster decompositions of f(N) are derived, one of which is essentially the multiplicity function. Subsidiary distribution functions for extremal distributions of f(N) are derived, and the generating function is used as a simple method for determining various statistical quantities such as means and moments. Compounded, filtered, and conditional forms of the distribution function are discussed, and their relation to observational selection and physical bias is examined. A spatial Kolmogorov equation is derived which gives the rate of change of f(N) with volume. 28 refs.
ISSN 0004637X
Educational Use Research
Learning Resource Type Article
Publisher Date 1989-06-01
Publisher Place United States
Journal Astrophysical Journal
Volume Number 341


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