Asymptotic laws for random knot diagrams

DOI10.1088/1751-8121/aa6e45zbMath1377.57023arXiv1608.02638OpenAlexW3104193093MaRDI QIDQ5272615

Harrison Chapman

Publication date: 30 June 2017

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.02638

zbMATH Keywords

knot diagramrandom maprandom knot, knot probability

Mathematics Subject Classification ID

Related Items (12)

A note on closed 3-braid knot shadows ⋮ The distribution of knots in the Petaluma model ⋮ Models of random knots ⋮ Crossing numbers of random two-bridge knots ⋮ A Markov Chain Sampler for Plane Curves ⋮ A lower bound on the average genus of a 2-bridge knot ⋮ Random colorings in manifolds ⋮ Structure and enumeration of \(K_4\)-minor-free links and link-diagrams ⋮ Mapping class group orbits of curves with self-intersections ⋮ On the Number of Unknot Diagrams ⋮ The tabulation of prime knot projections with their mirror images up to eight double points ⋮ The knots that lie above all shadows

Uses Software

• SciPy
• PLink

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariants of random knots and links
• Random knots using Chebyshev billiard table diagrams
• The self-avoiding walk.
• Loose, flat knots in collapsed polymers
• The asymptotic number of rooted maps on a surface
• State models and the Jones polynomial
• Submaps of maps. I: General 0-1 laws
• Polygon spaces and Grassmannians
• Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees
• Virtual knot theory
• Knots in random walks
• Planar diagrams
• Almost all maps are asymmetric
• On symmetric quadrangulations and triangulations
• Random sampling of large planar maps and convex polyhedra
• Knot probabilities in random diagrams
• Probability Theory of Random Polygons from the Quaternionic Viewpoint
• On the universality of knot probability ratios
• Off-lattice random walks with excluded volume: a new method of generation, proof of ergodicity and numerical results
• Maps, immersions and permutations
• Lattice knots in a slab
• A new polynomial invariant of knots and links
• Knots in self-avoiding walks
• Monte Carlo results for projected self-avoiding polygons: a two-dimensional model for knotted polymers
• GAUSSIAN RANDOM POLYGONS ARE GLOBALLY KNOTTED
• Random walks on braid groups: Brownian bridges, complexity and statistics
• Interacting self-avoiding walks and polygons in three dimensions
• A TRANSFER MATRIX APPROACH TO THE ENUMERATION OF KNOTS
• Verification of the Jones unknot conjecture up to 22 crossings
• The statistical mechanics of random copolymers
• On the Asymptotic Number of Plane Curves and Alternating Knots
• The Knotting of Equilateral Polygons in R³
• The expected total curvature of random polygons
• Links and Planar Diagram Codes
• On the Number of Self-Avoiding Walks. II
• MATRIX INTEGRALS AND THE GENERATION AND COUNTING OF VIRTUAL TANGLES AND LINKS
• Self-avoiding walks in a slab with attractive walls
• A Census of Planar Maps
• On the Number of Self-Avoiding Walks

This page was built for publication: Asymptotic laws for random knot diagrams