N-point function

The term N-point function (or N-point correlation function) is used in cosmology for functions that correlate values of some function on a surface according to their spatial distribution. The "N" indicates the number of values being correlated as follows:

• 1-point function - means statistics on the values of individual points, e.g., histograms, means, standard deviation.
• 2-point function (or 2-point correlation function) - an example is the angular power spectrum.
• 3-point function (or 3-point correlation function) - bispectrum - analogous to the power spectrum, but for three points.

Analogous functions are possible for 4 or more points.

They are also referred to as spatial correlation functions. They shows statistical properties of the values on a surface, in the case of astronomy, typically functions on celestial sphere or redshift space, e.g., the magnitude or intensity of some value (a magnitude or intensity of something, perhaps isolated through subtracting contributions of sources irrelevant to the phenomena under study), looking for patterns of interest. Among its uses in cosmology are analysis of the cosmic microwave background (CMB) and of galaxy distributions, and use of the general term correlation function is likely to mean specifically a 2-point function over the celestial sphere.

Such functions have uses in other branches of astronomy, e.g., using the bispectrum as part of some speckle suppression techniques.

The term N-point function is also used in quantum field theory, but I can't tell if there is any relation. I believe it is analogous but it is not over the surface of a sphere but over three-dimensional space (field) or possibly (four-dimensional) spacetime.