A Fast Direct Sampling Algorithm for Equilateral Closed Polygons

Abstract

Sampling equilateral closed polygons is of interest in the statistical study of ring polymers. Over the past 30 years, previous authors have proposed a variety of simple Markov chain algorithms (but have not been able to show that they converge to the correct probability distribution) and complicated direct samplers (which require extended-precision arithmetic to evaluate numerically unstable polynomials). We present a simple direct sampler which is fast and numerically stable, and analyze its runtime using a new formula for the volume of equilateral polygon space as a Dirichlet-type integral.

10 pages, 2 figures. Added Duplantier as coauthor; we now give the precise asymptotic complexity of the algorithm

References in corpus (2)

• On the Limits of Analogy Between Self-Avoidance and Topology-Driven Swelling of Polymer Loops
• The symplectic geometry of closed equilateral random walks in 3-space

Cited by in corpus (8)

• Statistical and hydrodynamic properties of topological polymers for various graphs showing enhanced short-range correlation
• Symplectic Geometry and Connectivity of Spaces of Frames
• Models of Random Knots
• Random Triangles and Polygons in the Plane
• Knot probabilities in equilateral random polygons
• New Stick Number Bounds from Random Sampling of Confined Polygons
• A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting
• CoBarS: Fast reweighted sampling for polygon spaces in any dimension