Some Classes of Probability Distributions

Abstract

The relevance of the previously introduced moment and correlation-type functionals can be illustrated by examples of some classical classes of probability distributions. In this chapter, these functionals are discussed for product measures (in which case one can also refine upper bounds on “small ball” probabilities), for joint distributions of pairwise independent random variables, and for coordinate-symmetric distributions. We also discuss the class of logarithmically concave measures and include some additional background material which will be needed later on.