In mathematics, the Fortuin–Kasteleyn–Ginibre (FKG) inequality is a correlation inequality, a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the probabilistic method), due to , Pieter W. Kasteleyn, and Jean Ginibre . Informally, it says that in many random systems, increasing events are positively correlated, while an increasing and a decreasing event are negatively correlated. It was obtained by studying the random cluster model.