Compound Poisson approximation for random fields with application to sequence alignment

The article presents the theory of stationary regularly varying random fields. In this context, we prove a new compound Poisson approximation theorem under appropriate dependence conditions, and demonstrate a couple of effective methods for checking its conditions. The theory is based on an extension of some standard point processes limiting theory to general Polish spaces. Finally, we apply these theoretical results to shed entirely new light on the classical problem of evaluating local alignments of biological sequences.