{"paper":{"title":"Scaling Limits for Minimal and Random Spanning Trees in Two Dimensions","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Almut Burchard, Charles M. Newman, David B. Wilson, Michael Aizenman","submitted_at":"1998-09-24T22:29:15Z","abstract_excerpt":"A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in $\\R^d$. Tightness of the distribution, as $\\delta \\to 0$, is established for the following two-dimensional examples: the uniformly random spanning tree on $\\delta \\Z^2$, the minimal spanning tree on $\\delta \\Z^2$ (with random edge lengths), and the Euclidean minimal spanning tree on a Poisson process of points in $\\R^2$ with density $\\delta^{-2}$. In each c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9809145","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"}