Editing Random field (section)

== Tensor-valued random fields ==

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. This leads to tensor-valued random fields{{what|reason=There is no indication here or in the linked Wikipedia article what these tensors might be.|date=October 2023}} in which the key role is played by a '''statistical volume element''' (SVE), which is a spatial box over which properties can be averaged; when the SVE becomes sufficiently large, its properties become deterministic and one recovers the [[representative volume element]] (RVE) of deterministic continuum physics. The second type of random field that appears in continuum theories are those of dependent quantities (temperature, displacement, velocity, deformation, rotation, body and surface forces, stress, etc.).<ref>{{cite book | author1=Malyarenko, Anatoliy |author2= Ostoja-Starzewski, Martin|authorlink2=Martin Ostoja-Starzewski |title=Tensor-Valued Random Fields for Continuum Physics | publisher=Cambridge University Press | year=2019 | isbn=9781108429856}}</ref>{{what|reason=What does "dependent" mean in this context? Is there supposed to be a dichotomy here between "tensor-valued" and "dependent"? Can't something be both or neither?|date=October 2023}}