Astrophysics (index)

N-Point Function

(N-Point Correlation Function, Spatial Correlation Function)
(general term for analyses-techniques of spatial data)

The term N-Point Function (or N-Point Correlation Function) is used in Cosmology for correlation functions that correlate values of a 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 - an example is the Angular Power Spectrum.
  • 3-Point 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, 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. While of cosmological interest, e.g., studying the Cosmic Microwave Background (CMB), it has potential in other areas of astronomical research. For example, the bispectrum is used in some Speckle Suppression techniques.

The term N-Point Function is also used in quantum mechanics, but I can't tell if there is any relation.