A Fast Direct Sampling Algorithm for Equilateral Closed Polygons
Statistical Mechanics
2019-10-23 v2 Probability
Symplectic Geometry
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.
Cite
@article{arxiv.1510.02466,
title = {A Fast Direct Sampling Algorithm for Equilateral Closed Polygons},
author = {Jason Cantarella and Bertrand Duplantier and Clayton Shonkwiler and Erica Uehara},
journal= {arXiv preprint arXiv:1510.02466},
year = {2019}
}
Comments
10 pages, 2 figures. Added Duplantier as coauthor; we now give the precise asymptotic complexity of the algorithm