Editing Random field (section)

{{Short description|Mathematical function}}
In [[physics]] and [[mathematics]], a '''random field''' is a random function over an arbitrary domain (usually a multi-dimensional space such as <math>\mathbb{R}^n</math>). That is, it is a function <math>f(x)</math> that takes on a random value at each point <math>x \in \mathbb{R}^n</math>(or some other domain). It is also sometimes thought of as a synonym for a [[stochastic process]] with some restriction on its index set. That is, by modern definitions, a random field is a generalization of a [[stochastic process]] where the underlying parameter need no longer be [[real coordinate space|real]] or [[integer]] valued "time" but can instead take values that are multidimensional [[vector space|vectors]] or points on some [[manifold]].<ref>{{cite book | author=Vanmarcke, Erik | title=Random Fields: Analysis and Synthesis | publisher=World Scientific Publishing Company | year=2010 | isbn=978-9812563538}}</ref>