Angular correlation function explained

The angular correlation function is a function which measures the projected clustering of galaxies, due to discrepancies between their actual and expected distributions.^[1] The function may be computed as follows:

w(\theta) = (1)/(N) (dP)/(d\Omega) -1 , where P represents the conditional probability of finding a galaxy, \Omega denotes the solid angle, and N is the mean number density. In a homogeneous universe, the angular correlation scales with a characteristic depth.^[2]

Notes and References

1. https://ui.adsabs.harvard.edu/abs/2005ApJ...619..147M/abstract The Galaxy Angular Correlation Functions and Power Spectrum from the Two Micron All Sky Survey
2. Web site: B. The correlation function: galaxies. 2021-06-09.