|
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, see (circulant 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.〔Peacock, John. ''Cosmological Physics'', Cambridge University Press, 1999. ISBN 0-521-41072-X 〕 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, ''x''1, ..., ''x''''N'', in the ''D''-dimensional space, then the vector (''f''(''x''1), ..., ''f''(''x''''N'')) will always be distributed as a multivariate Gaussian. An important special case of a GRF is the Gaussian free field. ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gaussian random field」の詳細全文を読む スポンサード リンク
|