Mathematics

In Probability, the FKG (short for Fortuin–Kasteleyn–Ginibre) Inequality is a correlation inequality and a fundamental tool in statistical mechanics and probabilistic combinatorics, especially random graphs with probabilistic method. In many random systems, increasing events are positively correlated, while an increasing and a decreasing event are negatively correlated.
In my talk, I will introduce my reading and research topics that is related to this inequality. Specifically I will start with the original version of this inequality, then apply its generalized form in other topics including 4-function theorem and percolation problem.