Meander, Folding and Arch Statistics

TL;DR

This paper explores the statistical properties of meanders and related folding problems in polymers, introducing recursive methods, matrix models, and exact solutions for simplified cases to deepen understanding of complex folding phenomena.

Contribution

It presents a novel recursive approach, links meander statistics to random matrix models, and provides exact solutions for related simplified folding problems.

Findings

Recursive relations for meander enumeration

Equivalence with random matrix models established

Exact solutions for arch configurations and irreducible meanders

Abstract

The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a direct recursive relation for building (semi) meanders (ii) the equivalence with a random matrix model (iii) the exact solution of simpler related problems, such as arch configurations or irreducible meanders.