A Markov Chain Sampler for Plane Curves

DOI10.1080/10586458.2019.1660739OpenAlexW2976033485MaRDI QIDQ5094488

Harrison Chapman, Andrew Rechnitzer

Publication date: 3 August 2022

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.03311

zbMATH Keywords

asymptoticsMarkov chainplanar mapsrandom knotsflat histogram

Mathematics Subject Classification ID

Computer science (68-XX) Combinatorics (05-XX)

Uses Software

• SnapPy

Cites Work

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• Invariants of random knots and links
• A classification of spherical curves based on Gauss diagrams
• A central limit theorem for the number of degree-\(k\) vertices in random maps
• A polynomial upper bound on Reidemeister moves
• Semiquandles and flat virtual knots
• The self-avoiding walk.
• Complexity of plane and spherical curves
• State models and the Jones polynomial
• A pattern of asymptotic vertex valency distributions in planar maps
• Shortening curves on surfaces
• Root vertex valency distributions of rooted maps and rooted triangulations
• Matrix integrals and the counting of tangles and links
• Making curves minimally crossing by Reidemeister moves
• Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees
• The rate of growth of the number of prime alternating links and tangles
• Untangling planar curves
• Knots in random walks
• The pivot algorithm: a highly efficient Monte Carlo method for the self-avoiding walk.
• The distribution of the maximum vertex degree in random planar maps
• Virtual knots and links
• Simple random walk on the uniform infinite planar quadrangulation: Subdiffusivity via pioneer points
• The number of Reidemeister moves needed for unknotting
• ON THE STRUCTURE AND SCARCITY OF ALTERNATING LINKS AND TANGLES
• Random sampling of large planar maps and convex polyhedra
• Knot probabilities in random diagrams
• On the universality of knot probability ratios
• Statistical topology of closed curves: Some applications in polymer physics
• Maps, immersions and permutations
• KNOTS, SLIPKNOTS, AND EPHEMERAL KNOTS IN RANDOM WALKS AND EQUILATERAL POLYGONS
• A new polynomial invariant of knots and links
• Infinitely Many Knots with the Same Polynomial Invariant
• Knots in self-avoiding walks
• Asymptotics of knotted lattice polygons
• The BFACF algorithm and knotted polygons
• Monte Carlo results for projected self-avoiding polygons: a two-dimensional model for knotted polymers
• The dimensions of knotted polygons
• On the Asymptotic Number of Plane Curves and Alternating Knots
• On knots in a model for the adsorption of ring polymers
• The Knotting of Equilateral Polygons in R³
• The geometry of spherical curves and the algebra of quaternions
• Equation of State Calculations by Fast Computing Machines
• Asymptotic laws for random knot diagrams