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Central and Local Limit Theorems for RNA Structures | | Emma Y. Jin
; Christian M. Reidys
; | | Date: |
1 Aug 2007 | | Abstract: | 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 numbers of 3-noncrossing RNA
structures over n nucleotides with exactly h bonds. We will build on the
results of cite{Reidys:07rna1} and cite{Reidys:07rna2}, where the generating
function of k-noncrossing RNA pseudoknot structures and the asymptotics for its
coefficients have been derived. The results of this paper explain the findings
on the numbers of arcs of RNA secondary structures obtained by molecular
folding algorithms and predict the distributions for k-noncrossing RNA folding
algorithms which are currently being developed. | | Source: | arXiv, 0707.4281 | | Services: | Forum | Review | PDF | Favorites | |
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