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.
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Famous quotes containing the words random and/or field:
“And catch the gleaming of a random light,
That tells me that the ship I seek is passing, passing.”
—Paul Laurence Dunbar (18721906)
“But the old world was restored and we returned
To the dreary field and workshop, and the immemorial feud
Of rich and poor. Our victory was our defeat.”
—Sir Herbert Read (18931968)