{"paper":{"title":"Uniform spanning forests associated with biased random walks on Euclidean lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"He Song, Kainan Xiang, Longmin Wang, Vladas Sidoravicius, Zhan Shi","submitted_at":"2018-05-04T05:35:53Z","abstract_excerpt":"The uniform spanning forest measure ($\\mathsf{USF}$) on a locally finite, infinite connected graph $G$ with conductance $c$ is defined as a weak limit of uniform spanning tree measure on finite subgraphs. Depending on the underlying graph and conductances, the corresponding $\\mathsf{USF}$ is not necessarily concentrated on the set of spanning trees. Pemantle~\\cite{PR1991} showed that on $\\mathbb{Z}^d$, equipped with the unit conductance $ c=1$, $\\mathsf{USF}$ is concentrated on spanning trees if and only if $d \\leq 4$. In this work we study the $\\mathsf{USF}$ associated with conductances induc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01615","kind":"arxiv","version":1},"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"}