{"paper":{"title":"The Minimum Perfect Matching in Pseudo-dimension $0<q<1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Joel Larsson","submitted_at":"2014-03-14T16:30:00Z","abstract_excerpt":"It is known that for $K_{n,n}$ equipped with i.i.d. $exp(1)$ edge costs, the minimum total cost of a perfect matching converges to $\\pi^2/6$ in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension $q \\geq 1$, such as Wei(1,q) costs. In this paper we extend those results all $q>0$, confirming the M\\'ezard-Parisi conjecture in the last remaining applicable case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3635","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"}