The paper considers interference in a wireless communication network caused by users that share the same propagation medium. Under the assumption that the interfering users are spatially Poisson distributed and under a power-law propagation loss function, it has been shown in the past that the interference instantaneous amplitude at the receiver is /spl alpha/-stable distributed. Past work has not considered the second-order statistics of the interference and has relied on the assumption that interference samples are independent. In this paper, we provide analytic expressions for the interference second-order statistics and show that depending on the properties of the users' holding times, the interference can be correlated. We provide conditions under which the interference becomes m-dependent, /spl phi/-mixing, or long-range dependent. Finally, we present some implications of our theoretical findings on signal detection.