{"paper":{"title":"The interaction of a gap with a free boundary in a two dimensional dimer system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Bloomington), Christian Krattenthaler (Universit\\\"at Wien), Mihai Ciucu (Indiana University","submitted_at":"2009-12-10T15:41:01Z","abstract_excerpt":"Let $\\ell$ be a fixed vertical lattice line of the unit triangular lattice in the plane, and let $\\Cal H$ be the half plane to the left of $\\ell$. We consider lozenge tilings of $\\Cal H$ that have a triangular gap of side-length two and in which $\\ell$ is a free boundary - i.e., tiles are allowed to protrude out half-way across $\\ell$. We prove that the correlation function of this gap near the free boundary has asymptotics $\\frac{1}{4\\pi r}$, $r\\to\\infty$, where $r$ is the distance from the gap to the free boundary. This parallels the electrostatic phenomenon by which the field of an electric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2023","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}