### 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 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 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 mechanics,
but I can't tell if there is any relation.

(*mathematics,statistics,cosmology*)
**Further reading:**

http://en.wikipedia.org/wiki/Correlation_function_(astronomy)

http://en.wikipedia.org/wiki/Bispectrum

**Referenced by pages:**

Athena

speckle masking

Index