{"paper":{"title":"Bi-orthogonal Polynomial Sequences and the Asymmetric Simple Exclusion Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.RA","math.RT"],"primary_cat":"math-ph","authors_text":"Richard Brak, William Moore","submitted_at":"2014-12-23T02:06:13Z","abstract_excerpt":"We reformulate the Corteel-Williams equations for the stationary state of the two parameter Asymmetric Simple Exclusion Process (TASEP) as a linear map $\\mathcal{L}(\\,\\cdot\\,)$, acting on a tensor algebra built from a rank two free module with basis $\\{e_1,e_2\\}$. From this formulation we construct a pair of sequences, $\\{P_n(e_1)\\}$ and $\\{Q_m(e_2)\\}$, of bi-orthogonal polynomials (BiOPS), that is, they satisfy $\\mathcal{L}(P_n(e_1)\\otimes Q_m(e_2))=\\Lambda_n\\delta_{n,m}$. The existence of the sequences arises from the determinant of a Pascal triangle like matrix of polynomials. The polynomia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7235","kind":"arxiv","version":2},"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"}