{"paper":{"title":"A Central Limit Theorem for the Optimal Alignments Score in Multiple Random Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Christian Houdr\\'e, Ruoting Gong, \\\"Umit I\\c{s}lak","submitted_at":"2015-12-17T17:59:06Z","abstract_excerpt":"Let $\\mathbf{X}^{(1)}_{n},\\ldots,\\mathbf{X}^{(m)}_{n}$, where $\\mathbf{X}^{(i)}_{n}=(X^{(i)}_{1},\\ldots,X^{(i)}_{n})$, $i=1,\\ldots,m$, be $m$ independent sequences of independent and identically distributed random variables taking their values in a finite alphabet $\\mathcal{A}$. Let the score function $S$, defined on $\\mathcal{A}^{m}$, be non-negative, bounded, permutation-invariant, and satisfy a bounded differences condition. Under a variance lower-bound assumption, a central limit theorem is proved for the optimal alignments score of the $m$ random words."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05699","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"}