{"paper":{"title":"Correlation function for generalized P\\'olya urns: Finite-size scaling analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"cond-mat.stat-mech","authors_text":"Masato Hisakado, Shintaro Mori","submitted_at":"2015-01-05T06:02:52Z","abstract_excerpt":"We describe a universality class of the transitions of a generalized P\\'{o}lya urn by studying the asymptotic behavior of the normalized correlation function $C(t)$ using finite-size scaling analysis. $X(1),X(2),\\cdots$ are the successive additions of a red (blue) ball [$X(t)=1\\,(0)$] at stage $t$ and $C(t)\\equiv \\mbox{Cov}(X(1),X(t+1))/\\mbox{Var}(X(1))$. Furthermore, $z(t)=\\sum_{s=1}^{t}X(s)/t$ represents the successive proportions of red balls in an urn to which, at the $t+1$-th stage, a red ball is added, [$X(t+1)=1$], with probability $q(z(t))=(\\tanh [J(2z(t)-1)+h]+1)/2,J\\ge 0$, and a blue"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00764","kind":"arxiv","version":3},"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"}