{"paper":{"title":"Treeable Graphings Are Local Limits of Finite Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Hosseini, Patrice Ossona de Mendez","submitted_at":"2016-01-21T10:29:11Z","abstract_excerpt":"Let $\\mathbf G$ be a graphing, that is a Borel graph defined by $d$ measure preserving involutions. We prove that if $\\mathbf G$ is {\\em treeable} then it arises as the local limit of some sequence $(G_n)_{n\\in\\mathbb{N}}$ of graphs with maximum degree at most $d$. This extends a result by Elek [G. Elek, Note on limits of finite graphs, Combinatorica 27 (2007)] (for $\\mathbf G$ a treeing) and consequently extends the domain of the graphings for which Aldous-Lyons conjecture is known to be true."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05580","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"}