Angular correlation function

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