A Gaussian random field is a spatially indexed Gaussian process; its law is determined by its mean and covariance kernel.
The Gaussian free field on a transient weighted graph is the centered Gaussian random field whose covariance kernel is the random walk Green function of a transient weighted graph.
Pinning a Gaussian free field at a vertex gives the field with value zero at and covarianceIt is independent of the removed scalar Gaussian mode at .
