Factor of IID

A factor of IID is a stochastic process obtained by applying a measurable equivariant rule to independent identically distributed labels. On a graph, place independent uniform labels in at the vertices and apply a rule that respects graph isomorphisms. The output may consist of vertex states or an edge configuration. For a fixed graph, equivariance means that relabeling by any graph automorphism relabels the output in the same way. The rule can depend on infinitely many input labels and need not be a finite-radius algorithm.