{"paper":{"title":"Lower bounds for moments of global scores of pairwise Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Zucca, Heinrich Matzinger, Joonas Sova, J\\\"uri Lember","submitted_at":"2016-02-17T20:23:43Z","abstract_excerpt":"Let $X_1,X_2,\\ldots$ and $Y_1,Y_2,\\ldots$ be two random sequences so that every random variable takes values in a finite set $\\mathbb{A}$. We consider a global similarity score $L_n:=L(X_1,\\ldots,X_n;Y_1,\\ldots,Y_n)$ that measures the homology (relatedness) of words $(X_1,\\ldots,X_n)$ and $(Y_1,\\ldots,Y_n)$. A typical example of such score is the length of the longest common subsequence. We study the order of central absolute moment $E|L_n-EL_n|^r$ in the case where two-dimensional process $(X_1,Y_1),(X_2,Y_2),\\ldots$ is a Markov chain on $\\mathbb{A}\\times \\mathbb{A}$. This is a very general m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05560","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"}