Weakly Associated Random Variables

The purposes of this chapter are to introduce the notion of weakly associated (negatively or positively) random variables and to develop tools that will allow us, in the chapters to follow, to give estimations of moments of partial sums, maximal inequalities, and asymptotic results with both Gaussian and non-gaussian limits. As we shall see, these results shed light on the asymptotic behavior of numerous examples such as exchangeable variables, certain Gaussian processes, empirical processes, various classes of Markov chains, and determinantal processes. They are also useful to study stochastic processes that are functionals of the two independent processes mentioned above.