the direction) between and , then the process is considered isotropic. A process that is concurrently stationary and isotropic is considered to be homogeneous; in practice these properties reflect the differences (or rather the lack of them) in the behaviour of the process given the location of the observer.

Ultimately Gaussian processes translate as taking priors on functions and the smoothness of these priors can be induced by the covariance function. If we expect that for "near-by" input points