Correlation functions and multifractal analysis for galaxy distribution

The Void Probability Function as a Statistical Indicator

Symposium - International Astronomical Union ◽

10.1017/s0074180900159327 ◽

1987 ◽

Vol 124 ◽

pp. 359-362

Author(s):

Marc Lachièze-Rey ◽

Sophie Maurogordato

Keyword(s):

Correlation Functions ◽

Statistical Models ◽

Probability Function ◽

Statistical Indicator ◽

Galaxy Distribution ◽

The Galaxy ◽

Statistical Indicators

Recent results concerning the galaxy distribution at scales < 100 h−1 Mpc (Ho = 100 h kms−1 Mpc−1) show a number of characteristics which cannot be described by conventional statistical models. Correlation functions, for instance, can in no way give account of the presence of voids of the cellular (or spongy) appearance of the local galaxy distribution (M. Geller, this conference). There is clearly a need for new kinds of statistical models and statistical indicators.

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n-Point Correlation Functions: Descriptive Statistics

The Large-Scale Structure of the Universe ◽

10.23943/princeton/9780691209838.003.0003 ◽

2020 ◽

pp. 138-256

Author(s):

P. J. E. Peebles

Keyword(s):

Correlation Functions ◽

Practical Importance ◽

Descriptive Statistics ◽

Statistical Estimates ◽

Galaxy Distribution ◽

Statistical Pattern ◽

The Galaxy ◽

Angular Correlation Function ◽

Point Correlation ◽

Simple Linear Equation

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.

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