{"paper":{"title":"Multivariate Kawtchouk polynomials as Birth and Death polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.CA","authors_text":"Ryu Sasaki","submitted_at":"2023-05-15T12:07:25Z","abstract_excerpt":"Multivariate Krawtchouk polynomials are constructed explicitly as Birth and Death polynomials, which have the nearest neighbour interactions. They form the complete set of eigenpolynomials of a birth and death process with the birth and death rates at population $x=(x_1,\\ldots,x_n)$ are $B_j(x)=\\bigl(N-\\sum_{i=1}^nx_i\\bigr)$ and $D_j(x)=p_i^{-1}x_j$, $0<p_j$, $j=1,\\ldots,n$. The corresponding stationary distribution is the multinomial distribution with the probabilities $\\{\\eta_i\\}$, $\\eta_i= p_i/(1+\\sum_{j=1}^np_j)$. The polynomials, depending on $n+1$ parameters ($\\{p_i\\}$ and $N$), satisfy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08581","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.08581/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"}