{"paper":{"title":"The Infinite Limit of Random Permutations Avoiding Patterns of Length Three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross G. Pinsky","submitted_at":"2018-06-20T11:30:44Z","abstract_excerpt":"For $\\tau\\in S_3$, let $\\mu_n^{\\tau}$ denote the uniformly random probability measure on the set of $\\tau$-avoiding permutations in $S_n$. Let $\\mathbb{N}^*=\\mathbb{N}\\cup\\{\\infty\\}$ with an appropriate metric and denote by\n  $S(\\mathbb{N},\\mathbb{N}^*)$ the compact metric space consisting of functions $\\sigma=\\{\\sigma_i\\}_{ i=1}^\\infty$ from $\\mathbb{N}$ to $\\mathbb{N}^*$ which are injections when restricted to $\\sigma^{-1}(\\mathbb{N})$\\rm; that is, if $\\sigma_i=\\sigma_j$, $i\\neq j$, then $\\sigma_i=\\infty$. Extending permutations $\\sigma\\in S_n$ by defining $\\sigma_j=j$, for $j>n$, we have $S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07669","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"}