Gaussian Process

A Gaussian process is a family of random variables whose every finite linear combination has a normal distribution, with degenerate distributions allowed. It is determined by its mean function and covariance function

For example, if is standard normal and is a deterministic function, then is a Gaussian process with covariance . A Gaussian free field uses an analogous Gaussian family indexed by test functions. The Gaussian Sherrington-Kirkpatrick model Hamiltonian is a Gaussian process indexed by spin configurations because its coefficients are Gaussian and it is linear in those coefficients. Applying nonlinear functions to Gaussian pattern measurements in a random perceptron does not generally give a Gaussian process.