{"paper":{"title":"Coalescence of Geodesics in Exactly Solvable Models of Last Passage Percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Allan Sly, Riddhipratim Basu, Sourav Sarkar","submitted_at":"2017-04-18T07:14:11Z","abstract_excerpt":"Coalescence of semi-infinite geodesics remains a central question in planar first passage percolation. In this paper we study finer properties of the coalescence structure of finite and semi-infinite geodesics for exactly solvable models of last passage percolation. Consider directed last passage percolation on $\\mathbb{Z}^2$ with i.i.d. exponential weights on the vertices. Fix two points $v_1=(0,0)$ and $v_2=(0, \\lfloor k^{2/3} \\rfloor)$ for some $k>0$, and consider the maximal paths $\\Gamma_1$ and $\\Gamma_2$ starting at $v_1$ and $v_2$ respectively to the point $(n,n)$ for $n\\gg k$. Our obje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05219","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"}