A random field is a generalization of a stochastic process such that the underlying parameter need no longer be a simple real or integer valued "time", but can instead take values that are multidimensional vectors, or points on some manifold.
At its most basic, discrete case, a random field is a list of random numbers whose indices are mapped onto a space (of n dimensions). Values in a random field are usually spatially correlated in one way or another. In its most basic form this might mean that adjacent values (i.e. values with adjacent indices) do not differ as much as values that are further apart. This is an example of a covariance structure, many different types of which may be modeled in a random field. More generally, the values might be defined over a continuous domain, and the random field might be thought of as a "function valued" random variable.
Other articles related to "random, random field, random fields":
... process Branching process Branching random walk Brownian bridge Brownian motion Chinese restaurant process CIR process Continuous stochastic process ... theorem Lévy process Local time (mathematics) Loop-erased random walk Markov processes are those in which the future is conditionally independent of the past given the present ... Ornstein–Uhlenbeck process Point processes random arrangements of points in a space ...
... Kriging interpolates the value of a random field (e.g ... of the geographic location ) at an unobserved location from observations of the random field at nearby locations ... and the covariance function of the random field ...
... Random fields are of great use in studying natural processes by the Monte Carlo method, in which the random fields correspond to naturally spatially varying properties, such as soil permeability over the ... A further common use of random fields is in the generation of computer graphics, particularly those that mimic natural surfaces such as water and earth ...
Famous quotes containing the words field and/or random:
“An enormously vast field lies between God exists and there is no God. The truly wise man traverses it with great difficulty. A Russian knows one or the other of these two extremes, but is not interested in the middle ground. He usually knows nothing, or very little.”
—Anton Pavlovich Chekhov (18601904)
“Novels as dull as dishwater, with the grease of random sentiments floating on top.”
—Italo Calvino (19231985)