If just one random galaxy is chosen, then the definition is no longer correct, firstly because it is meaningless to talk of just one "random" galaxy, and secondly because the function will vary wildly depending on which galaxy is chosen, in contradiction with its definition as a function. The following definition is often cited: In astronomy, a correlation function describes the distribution of galaxies in the universe. However, it can only be correct in the statistical sense that it is averaged over a large number of galaxies chosen as the first, random galaxy. It can be thought of as a lumpiness factor - the higher the value for some distance scale, the more lumpy the universe is at that distance scale. For a given distance, the two-point autocorrelation function is a function of one variable which describes the probability that two galaxies are separated by this particular distance. By default, correlation function refers to the two-point autocorrelation function. High Quality Content by WIKIPEDIA articles! Given a random galaxy in a location, the correlation function describes the probability that another galaxy will be found within a given distance.
Correlation Function (Astronomy)
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