Central and local limit theorems for RNA structures.

Large deviations of combinatorial distributions II: Local limit theorems

This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations1 applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables {Ωn}n≥1 each of maximal span 1 (see below for definition), we a...

Central and Local Limit Theories in Markov Dependent Random Variables

On Convergence Rates in the Central Limit Theorems for Combinatorial Structures

Flajolet and Soria established several central limit theorems for the parameter “number of components” in a wide class of combinatorial structures. In this paper, we shall prove a simple theorem which applies to characterize the convergence rates in their central limit theorems. This theorem is also applicable to arithmetical functions. Moreover, asymptotic expressions are derived for moments o...

Loops in Canonical RNA Pseudoknot Structures

In this article, we compute the limit distributions of the numbers of hairpin-loops, interior-loops and bulges in k-noncrossing RNA structures. The latter are coarse-grained RNA structures allowing for cross-serial interactions, subject to the constraint that there are at most k - 1 mutually crossing arcs in the diagram representation of the molecule. We prove central limit theorems by means of...

Central and Local Limit Theorems for Excedances by Conjugacy Class and by Derangement

We give central and local limit theorems for the number of excedances of a uniformly distributed random permutation belonging to certain sequences of conjugacy classes and belonging to the sequence of derangements.