Sparse stable configurations of hard discs in a box
Metric Geometry
2010-11-01 v3 Combinatorics
Probability
Abstract
We construct stable configurations of n overlapping discs of radius r in a unit square, with r = O(1/n). By a result of Diaconis, Lebeau, and Michel, this result is best possible, up to a constant factor. A consequence is that the Metropolis algorithm, a well-studied Markov chain on the hardcore model, is not irreducible in this range of parameters.
Keywords
Cite
@article{arxiv.0908.1830,
title = {Sparse stable configurations of hard discs in a box},
author = {Matthew Kahle},
journal= {arXiv preprint arXiv:0908.1830},
year = {2010}
}
Comments
10 pages; 8 figures -- minor revisions