{"paper":{"title":"Thermodynamic Limit for the Mallows Model on $S_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Shannon Starr","submitted_at":"2009-04-04T20:18:04Z","abstract_excerpt":"The Mallows model on $S_n$ is a probability distribution on permutations, $q^{d(\\pi,e)}/P_n(q)$, where $d(\\pi,e)$ is the distance between $\\pi$ and the identity element, relative to the Coxeter generators. Equivalently, it is the number of inversions: pairs $(i,j)$ where $1\\leq i<j\\leq n$, but $\\pi_i>\\pi_j$. Analyzing the normalization $P_n(q)$, Diaconis and Ram calculated the mean and variance of $d(\\pi,e)$ in the Mallows model, which suggests the appropriate $n \\to \\infty$ limit has $q_n$ scaling as $1-\\beta/n$. We calculate the distribution of the empirical measure in this limit, $u(x,y) dx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0696","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"}