{"paper":{"title":"A Monte Carlo Approach to the Fluctuation Problem in Optimal Alignments of Random Strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Heinrich Matzinger, Raphael Hauser, Saba Amsalu","submitted_at":"2012-11-23T12:57:25Z","abstract_excerpt":"The problem of determining the correct order of fluctuation of the optimal alignment score of two random strings of length $n$ has been open for several decades. It is known that the biased expected effect of a random letter-change on the optimal score implies an order of fluctuation linear in $\\sqrt{n}$. However, in many situations where such a biased effect is observed empirically, it has been impossible to prove analytically. The main result of this paper shows that when the rescaled-limit of the optimal alignment score increases in a certain direction, then the biased effect exists. On the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5489","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":""},"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"}