Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
1998
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/9801068 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910107959296000 |
|---|---|
| author | Jockusch, William Propp, James Shor, Peter |
| author_facet | Jockusch, William Propp, James Shor, Peter |
| contents | In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby tiles, while in the fifth, central sub-region, differently-oriented tiles co-exist side by side. We show that when n is sufficiently large, the shape of the central sub-region becomes arbitrarily close to a perfect circle of radius n/sqrt(2) for all but a negligible proportion of the tilings. Our proof uses techniques from the theory of interacting particle systems. In particular, we prove and make use of a classification of the stationary behaviors of a totally asymmetric one-dimensional exclusion process in discrete time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9801068 |
| institution | arXiv |
| publishDate | 1998 |
| record_format | arxiv |
| spellingShingle | Random Domino Tilings and the Arctic Circle Theorem Jockusch, William Propp, James Shor, Peter Combinatorics 60C05 In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby tiles, while in the fifth, central sub-region, differently-oriented tiles co-exist side by side. We show that when n is sufficiently large, the shape of the central sub-region becomes arbitrarily close to a perfect circle of radius n/sqrt(2) for all but a negligible proportion of the tilings. Our proof uses techniques from the theory of interacting particle systems. In particular, we prove and make use of a classification of the stationary behaviors of a totally asymmetric one-dimensional exclusion process in discrete time. |
| title | Random Domino Tilings and the Arctic Circle Theorem |
| topic | Combinatorics 60C05 |
| url | https://arxiv.org/abs/math/9801068 |