{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [
    "SC-B Consulting, Urbana, USA",
    "Wizards of the Coast",
    "University of Massachusetts Lowell, USA",
    "MIT",
    "Massachusetts Institute of Technology, Cambridge, USA",
    "AT&T-Labs"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "William Jockusch"
    },
    {
      "affs": [
        2,
        3
      ],
      "name": "James Gary Propp",
      "orcid": "0000-0002-0913-3649"
    },
    {
      "affs": [
        4,
        5
      ],
      "name": "Peter W. Shor",
      "orcid": "0000-0003-4626-5648"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dekpnh5qhktj.bib",
  "cited_by": 224,
  "doi": "10.4171/aihpd/233",
  "fulltext_url": null,
  "id": "3dekpnh5qhktj",
  "issns": [
    "2308-5827",
    "2308-5835"
  ],
  "landing_url": "https://doi.org/10.4171/aihpd/233",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W1508356799",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-11",
  "publisher": "EMS Press",
  "ris": "https://research.draconitic.com/paper/3dekpnh5qhktj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W1508356799",
      "source": "openalex",
      "url": "https://doi.org/10.4171/aihpd/233"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Random domino tilings and the arctic circle theorem",
  "title_text": "Random domino tilings and the arctic circle theorem",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:41Z",
  "url": "https://research.draconitic.com/paper/3dekpnh5qhktj",
  "venue": "Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions",
  "versions": []
}