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Title: Some properties of a statistical distribution function for galaxy clustering

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.

Authors:
 [1]
  1. National Radio Astronomy Observatory, Charlottesville, VA (USA)
Publication Date:
OSTI Identifier:
5642878
Resource Type:
Journal Article
Journal Name:
Astrophysical Journal; (USA)
Additional Journal Information:
Journal Volume: 341; Journal ID: ISSN 0004-637X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GALAXY CLUSTERS; DISTRIBUTION FUNCTIONS; ASTROPHYSICS; GRAVITATION; KOLMOGOROV EQUATION; MANY-BODY PROBLEM; STOCHASTIC PROCESSES; THERMODYNAMICS; DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; 640105* - Astrophysics & Cosmology- Galaxies

Citation Formats

Saslaw, W C, and Cambridge Univ. Some properties of a statistical distribution function for galaxy clustering. United States: N. p., 1989. Web. doi:10.1086/167519.
Saslaw, W C, & Cambridge Univ. Some properties of a statistical distribution function for galaxy clustering. United States. doi:10.1086/167519.
Saslaw, W C, and Cambridge Univ. Thu . "Some properties of a statistical distribution function for galaxy clustering". United States. doi:10.1086/167519.
@article{osti_5642878,
title = {Some properties of a statistical distribution function for galaxy clustering},
author = {Saslaw, W C and Cambridge Univ.},
abstractNote = {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.},
doi = {10.1086/167519},
journal = {Astrophysical Journal; (USA)},
issn = {0004-637X},
number = ,
volume = 341,
place = {United States},
year = {1989},
month = {6}
}