Gaussian random field
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In statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional 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
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
Suppose f(x) is the value of a GRF at a point x in some D-dimensional space. If we make a vector of the values of f at N points, x1, ..., xN, in the D-dimensional space, then the vector (f(x1), ..., f(xN)) will always be distributed as a multivariate Gaussian.
See also
References
- ISBN 0-521-41072-X – via Google Books.
External links
- For details on the generation of Gaussian random fields using Matlab, see circulant embedding method for Gaussian random field.
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