Conjugate Cumulant and Moment Inequalities

Abstract

It is well-known that the relationship between multivariate moment and multivariate cumulant is described in terms of combinatorics such as partition lattice and associated Mobius function. In this talk, we define "conjugate cumulant" so that it has dual properties to the original cumulant. Using the conjugate cumulant, a class of moment inequalities is proved. A conjecture about higher-order FKG inequalities is mentioned, which is the motivation of defining the conjugate cumulant. (This is a joint work with Donald Richards, Penn State Univ.)