Gaussian random fields

Abstract

Gaussian random fields have a long history in science that dates back to the research of Andrey Kolmogorov and his group. Their investigation remains an active field of research with many applications in physics and engineering. The widespread appeal of Gaussian random fields is due to convenient mathematical simplifications that they enable, such as the decomposition of many-point correlation functions into products of two-point correlation functions. The simplifications achieved by Gaussian random fields are based on fact that the joint Gaussian probability density function is fully determined by the mean and the covariance function.