Sparse stable configurations of hard discs in a box
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2009
- DOI:
- 10.48550/arXiv.0908.1830
- arXiv:
- arXiv:0908.1830
- Bibcode:
- 2009arXiv0908.1830K
- Keywords:
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- Mathematics - Metric Geometry;
- Mathematics - Combinatorics;
- Mathematics - Probability;
- 52C15;
- 60J22
- E-Print:
- 10 pages