{
  "abstract": "We study local $2\\times2$ correlations in uniformly random domino tilings of the Aztec diamond $\\mathrm{AZ}(n)$, a dimer model with frozen corners and a liquid region bounded by the Arctic circle, and compare them with the square chessboard. For every elementary square the probabilities $P_H$ and $P_V$ of the two coverings by a pair of parallel dominoes satisfy $P_H=P_V=P_1P_2+P_3P_4$, where $P_1,\\dots,P_4$ are the probabilities of the four surrounding edges. This known identity, a case of Kuo's graphical condensation, reduces the spatial profile of $P_H$ to single-edge probabilities, which we compute exactly from the inverse Kasteleyn matrix for all squares of $\\mathrm{AZ}(n)$. The squares form two interleaved sublattices, distinguished by the color of their lower-left cell. The parity of $n$ decides which sublattice dominates near the center: the one containing the central square for odd $n$, and the other one for even $n$. This sign rule holds for the averaged sublattice contrast for all $4\\le n\\le22$. It also fixes the location of the global maximum of $P_H$, which lies at or next to the center for odd $n$ and several lattice spacings away for even $n$. Within the central sublattice, the preferred square follows a mod-4 pattern that matches the exactly pinned mean height of the center. On the $L\\times L$ chessboard the same rule holds with $n$ replaced by the half-width $L/2$, but the contrast is two to six times weaker, the central edge probability never equals $1/4$, and the maxima of $P_H$ are pinned to the corners. The exact $1/4$ values and the interior, parity-selected maxima are therefore features of the Aztec geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22974",
  "author_total": 5,
  "authors": [
    {
      "name": "Chaeyeon Kim"
    },
    {
      "name": "Suhwan Yoo"
    },
    {
      "name": "Jeehoon Choi"
    },
    {
      "name": "Hee Young Kwon"
    },
    {
      "name": "Changyeon Won"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/69vg0ecnq30vc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22974",
  "fulltext_url": null,
  "id": "69vg0ecnq30vc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22974",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7222942620",
  "pdf_url": "https://arxiv.org/pdf/2610.22974",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/69vg0ecnq30vc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.22974",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22974"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Parity-dependent sublattice structure of local $2\\times2$ correlations in domino tilings of the Aztec diamond",
  "title_text": "Parity-dependent sublattice structure of local 2×2 correlations in domino tilings of the Aztec diamond",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/69vg0ecnq30vc",
  "venue": "arXiv",
  "versions": []
}