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The Large-Scale Structure of the Universe$
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P. J. E. Peebles

Print publication date: 2020

Print ISBN-13: 9780691209838

Published to Princeton Scholarship Online: May 2021

DOI: 10.23943/princeton/9780691209838.001.0001

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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 18 May 2022

n-Point Correlation Functions: Descriptive Statistics

n-Point Correlation Functions: Descriptive Statistics

Chapter:
(p.138) III n-Point Correlation Functions: Descriptive Statistics
Source:
The Large-Scale Structure of the Universe
Author(s):

P. J. E. Peebles

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691209838.003.0003

This chapter explores the statistical pattern of the galaxy distribution. It focuses on n-point correlation functions (analogs of the autocorrelation function and higher moments for a continuous function), the descriptive statistics that have proved useful. The approach has also proved useful in many other applications. Of considerable practical importance has been the fact that there is a simple linear equation relating the directly observable angular correlation function to the wanted spatial function. This means the translation from one to the other is fairly easy, and equally important it makes it easy to say how the statistical estimates ought to scale with the depth of the survey and hence to test for possible contamination of the estimates by systematic errors. A third useful result is that the dynamics of the galaxy distribution can be treated in terms of the mass correlation functions: the statistic that proves useful for the reduction of the data may also be useful for the analysis of the theory.

Keywords:   galaxy distribution, n-point correlation functions, autocorrelation function, linear equation, mass correlation functions, descriptive statistics

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