Central and local limit theorems for RNA structures.

A k-noncrossing RNA pseudoknot structure is a graph over {1,...,n} without 1-arcs, i.e. arcs of the form (i,i+1) and in which there exists no k-set of mutually intersecting arcs. In particular, RNA secondary structures are 2-noncrossing RNA structures. In this paper we prove a central and a local limit theorem for the distribution of the number of 3-noncrossing RNA structures over n nucleotides with exactly h bonds. Our analysis employs the generating function of k-noncrossing RNA pseudoknot structures and the asymptotics for the coefficients. The results of this paper explain the findings on the number of arcs of RNA secondary structures obtained by molecular folding algorithms and are of relevance for prediction algorithms of k-noncrossing RNA structures.