A Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A onedimensional GRF is also called a Gaussian process. An important special case of a GRF is the Gaussian free field.
With regard to applications of GRFs, the initial conditions of physical cosmology generated by quantum mechanical fluctuations during cosmic inflation are thought to be a GRF with a nearly scale invariant spectrum.^{[1]}
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✪ 6.2 Gaussian Markov Random Fields (GMRF)  Image Analysis Class 2013

✪ 15.1 Gaussian Markov Random Fields  Image Analysis Class 2015

✪ 6.1 Markov Random Fields (MRFs)  Image Analysis Class 2013
Transcription
Construction
One way of constructing a GRF is by assuming that the field is the sum of a large number of plane, cylindrical or spherical waves with uniformly distributed random phase. Where applicable, the central limit theorem dictates that at any point, the sum of these individual planewave contributions will exhibit a Gaussian distribution. This type of GRF is completely described by its power spectral density, and hence, through the WienerKhinchin theorem, by its twopoint autocorrelation function, which is related to the power spectral density through a Fourier transformation.
Suppose f(x) is the value of a GRF at a point x in some Ddimensional space. If we make a vector of the values of f at N points, x_{1}, ..., x_{N}, in the Ddimensional space, then the vector (f(x_{1}), ..., f(x_{N})) will always be distributed as a multivariate Gaussian.
References
 ^ Peacock, John. Cosmological Physics, Cambridge University Press, 1999. ISBN 052141072X^{[page needed]}
External links
 For details on the generation of Gaussian random fields using Matlab, see circulant embedding method for Gaussian random field.