{"paper":{"title":"Active spanning trees and Schramm-Loewner evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adrien Kassel, David B. Wilson","submitted_at":"2015-12-30T20:52:23Z","abstract_excerpt":"We consider the Peano curve separating a spanning tree from its dual spanning tree on an embedded planar graph, where the tree and dual tree are weighted by $y$ to the number of active edges, and \"active\" is in the sense of the Tutte polynomial. When the graph is a portion of the square grid approximating a simply connected domain, it is known ($y=1$ and $y=1+\\sqrt{2}$) or believed ($1<y<3$) that the Peano curve converges to a space-filling SLE$_{\\kappa}$ loop, where $y=1-2\\cos(4\\pi/\\kappa)$, corresponding to $4<\\kappa\\leq 8$. We argue that the same should hold for $0\\le y<1$, which correspond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09122","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"}