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- Gaussian_random_field abstract "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.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 plane-wave contributions will exhibit a Gaussian distribution. This type of GRF is completely described by its power spectral density, and hence, through the Wiener-Khinchin theorem, by its two-point autocorrelation function, which is related to the power spectral density through a Fourier transformation. For details on the generation of Gaussian random fields using Matlab, seecirculant embedding method for Gaussian random 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.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.An important special case of a GRF is the Gaussian free field.[citation needed]".
- Gaussian_random_field wikiPageExternalLink 38880-circulant-embedding-method-for-generating-stationary-gaussian-field.
- Gaussian_random_field wikiPageID "1803858".
- Gaussian_random_field wikiPageRevisionID "530800050".
- Gaussian_random_field hasPhotoCollection Gaussian_random_field.
- Gaussian_random_field subject Category:Spatial_processes.
- Gaussian_random_field type Abstraction100002137.
- Gaussian_random_field type Act100030358.
- Gaussian_random_field type Activity100407535.
- Gaussian_random_field type Event100029378.
- Gaussian_random_field type Procedure101023820.
- Gaussian_random_field type PsychologicalFeature100023100.
- Gaussian_random_field type SpatialProcesses.
- Gaussian_random_field type YagoPermanentlyLocatedEntity.
- Gaussian_random_field comment "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.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.".
- Gaussian_random_field label "Gaussian random field".
- Gaussian_random_field sameAs m.05y8fh.
- Gaussian_random_field sameAs Q5527848.
- Gaussian_random_field sameAs Q5527848.
- Gaussian_random_field sameAs Gaussian_random_field.
- Gaussian_random_field wasDerivedFrom Gaussian_random_field?oldid=530800050.
- Gaussian_random_field isPrimaryTopicOf Gaussian_random_field.