{"paper":{"title":"The $q^{\\mathrm{Volume}}$ lozenge tiling model via non-Hermitian orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Ahmad Barhoumi, Maurice Duits","submitted_at":"2025-04-23T18:40:49Z","abstract_excerpt":"We consider the $q^\\text{Volume}$ lozenge tiling model on a large, finite hexagon. It is well-known that random lozenge tilings of the hexagon correspond to a two-dimensional determinantal point process via a bijection with ensembles of non-intersecting paths. The starting point of our analysis is a formula for the correlation kernel due to Duits and Kuijlaars which involves the Christoffel-Darboux kernel of a particular family of non-Hermitian orthogonal polynomials. Our main results are split into two parts: the first part concerns the family of orthogonal polynomials, and the second concern"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.17042","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.17042/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}