{"paper":{"title":"Geometry and percolation on half planar triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gourab Ray","submitted_at":"2013-12-11T07:44:19Z","abstract_excerpt":"We analyze the geometry of domain Markov half planar triangulations. In \\cite{AR13} it is shown that there exists a one-parameter family of measures supported on half planar triangulations satisfying translation invariance and domain Markov property. We study the geometry of these maps and show that they exhibit a sharp phase-transition in view of their geometry at $\\alpha = 2/3$. For $\\alpha<2/3$, the maps form a tree-like stricture with infinitely many small cut-sets. For $\\alpha > 2/3$, we obtain maps of hyperbolic nature with exponential growth and anchored expansion. Some results about th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3055","kind":"arxiv","version":2},"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"}