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:
“Man always made, and still makes, grotesque blunders in selecting and measuring forces, taken at random from the heap, but he never made a mistake in the value he set on the whole, which he symbolized as unity and worshipped as God. To this day, his attitude towards it has never changed, though science can no longer give to force a name.”
—Henry Brooks Adams (1838–1918)
“Last night I watched my brothers play,
The gentle and the reckless one,
In a field two yards away.
For half a century they were gone
Beyond the other side of care
To be among the peaceful dead.”
—Edwin Muir (1887–1959)