Meander, Folding and Arch Statistics

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.

82 pages, uuencoded, uses harvmac (l mode) and epsf, 26+7 figures included

References in corpus (1)

• 2D Gravity and Random Matrices

Cited by in corpus (40)

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• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Hermitian Matrix Model with Plaquette Interaction
• Coloring Random Triangulations
• Rotational Symmetry Breaking in Multi-Matrix Models
• A transfer matrix approach to the enumeration of plane meanders
• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
• Kontsevich-Witten Model From 2+1 Gravity: New Exact Combinatorial Solution
• Fully Packed O(n=1) Model on Random Eulerian Triangulations
• New Integrable Lattice Models From Fuss-Catalan Algebras
• Partial transpose of random quantum states: exact formulas and meanders
• SU(N) Meander Determinants
• Enumeration of meanders and Masur-Veech volumes
• Hamiltonian Cycles on Random Eulerian Triangulations
• A growth model for RNA secondary structures
• Folding the Square-Diagonal Lattice
• Exact Meander Asymptotics: a Numerical Check
• Exactly solvable flat-foldable quadrilateral origami tilings
• Supersymmetric Matrix Models and the Meander Problem
• Additivity rates and PPT property for random quantum channels
• Folding Transitions of the Square-Diagonal Lattice
• Enumerating meandric systems with large number of loops
• Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of NC(n)
• Geometrically Constrained Statistical Models on Fixed and Random Lattices: From Hard Squares to Meanders
• Asymptotics of lieanders with fixed composition sizes
• Phase transitions and random matrices
• Functionals of the Free Brownian Bridge
• Applications of Supersymmetric Matrix Models
• Idempotents and homology of diagram algebras
• Meanders, hyperelliptic pillowcase covers, and the Johnson filtration
• The Gauss map of polyhedral vertex stars
• Free probability aspect of irreducible meander systems, and some related observations about meanders
• On the complexity of meander-like diagrams of knots
• Higher genus meanders and Masur-Veech volumes
• Generating series and matrix models for meandric systems with one shallow side