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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.".
- Gaussian_random_field wikiPageExternalLink 38880-circulant-embedding-method-for-generating-stationary-gaussian-field.
- Gaussian_random_field wikiPageID "1803858".
- Gaussian_random_field wikiPageLength "2144".
- Gaussian_random_field wikiPageOutDegree "13".
- Gaussian_random_field wikiPageRevisionID "667907139".
- Gaussian_random_field wikiPageWikiLink Autocorrelation.
- Gaussian_random_field wikiPageWikiLink Category:Spatial_processes.
- Gaussian_random_field wikiPageWikiLink Central_limit_theorem.
- Gaussian_random_field wikiPageWikiLink Gaussian_free_field.
- Gaussian_random_field wikiPageWikiLink Gaussian_process.
- Gaussian_random_field wikiPageWikiLink Inflation_(cosmology).
- Gaussian_random_field wikiPageWikiLink Multivariate_normal_distribution.
- Gaussian_random_field wikiPageWikiLink Physical_cosmology.
- Gaussian_random_field wikiPageWikiLink Quantum_fluctuation.
- Gaussian_random_field wikiPageWikiLink Random_field.
- Gaussian_random_field wikiPageWikiLink Scale_invariance.
- Gaussian_random_field wikiPageWikiLink Spectral_density.
- Gaussian_random_field wikiPageWikiLink Wiener–Khinchin_theorem.
- Gaussian_random_field wikiPageWikiLinkText "Gaussian random field".
- Gaussian_random_field wikiPageWikiLinkText "Gaussian".
- Gaussian_random_field wikiPageUsesTemplate Template:Authority_control.
- Gaussian_random_field wikiPageUsesTemplate Template:Citation_needed.
- Gaussian_random_field wikiPageUsesTemplate Template:Context.
- Gaussian_random_field wikiPageUsesTemplate Template:Probability-stub.
- Gaussian_random_field wikiPageUsesTemplate Template:Reflist.
- Gaussian_random_field wikiPageUsesTemplate Template:Stochastic_processes.
- Gaussian_random_field subject Category:Spatial_processes.
- Gaussian_random_field hypernym Field.
- Gaussian_random_field type Page.
- Gaussian_random_field type Process.
- Gaussian_random_field type Thing.
- 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 Q5527848.
- Gaussian_random_field sameAs m.05y8fh.
- Gaussian_random_field sameAs Q5527848.
- Gaussian_random_field wasDerivedFrom Gaussian_random_field?oldid=667907139.
- Gaussian_random_field isPrimaryTopicOf Gaussian_random_field.