{"paper":{"title":"Free Askey--Wilson functionals and geometric last passage percolation on a strip","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jacek Wesolowski, Kamil Szpojankowski, Wlodek Bryc","submitted_at":"2025-06-02T17:09:43Z","abstract_excerpt":"Barraquand, Corwin, and Yang arXiv:2306.05983 established that geometric last passage percolation (LPP) on a strip of $\\mathbb{Z}^2$ has a unique stationary measure. Building on this, Barraquand arXiv:2409.08927 derived explicit contour integral formulas for the model's multipoint probability generating function. In this paper, we introduce free Askey--Wilson functionals and use them to extend these generating function formulas. Our framework yields explicit expressions valid over a broader range of boundary parameters than previously accessible. This generalization allows us to determine the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01879","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/2506.01879/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"}