Gaussian free field

Summary

The Gaussian free field is a random function whose law is Gaussian, with covariance given by the Green function of the Laplacian. In the continuum it is a random generalised function rather than a function. It is the natural Gaussian analogue of a harmonic function with random fluctuations. In two dimensions the continuum field is conformally invariant and log-correlated. It appears in statistical physics, in random surfaces and in the theory of the Schramm–Loewner evolution.