Sparse stable configurations of hard discs in a box

Details Sparse stable configurations of hard discs in a box Sparse stable configurations of hard discs in a box

2009-08-13

arxiv.org/abs/0908.1830v3

Mathematics

Metric Geometry

10 pages; 8 figures -- minor revisions

Scientific paper

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.

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