{"paper":{"title":"Local limits of random spanning trees in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Luca Makowiec","submitted_at":"2024-10-22T09:15:01Z","abstract_excerpt":"We study the edge overlap and local limit of the random spanning tree in random environment (RSTRE) on the complete graph with $n$ vertices and weights given by $\\exp(-\\beta \\omega_e)$ for $\\omega_e$ uniformly distributed on $[0,1]$. We show that for $\\beta$ growing with $\\beta = o(n/\\log n)$, the edge overlap is $(1+o(1)) \\beta$, while for $\\beta$ much larger than $n \\log^2 n$, the edge overlap is $(1-o(1))n$. Furthermore, there is a transition of the local limit around $\\beta = n$. When $\\beta = o(n/ \\log n)$ the RSTRE locally converges to the same limit as the uniform spanning tree, whereas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.16836","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.16836/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}