{"paper":{"title":"Brownian Web in the Scaling Limit of Supercritical Oriented Percolation in Dimension 1+1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anish Sarkar, Rongfeng Sun","submitted_at":"2011-08-05T06:02:07Z","abstract_excerpt":"We prove that, after centering and diffusively rescaling space and time, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2_{even}:={(x,i) in Z^2: x+i is even} converges in distribution to the Brownian web. This proves a conjecture of Wu and Zhang. Our key observation is that each rightmost infinite open path can be approximated by a percolation exploration cluster, and different exploration clusters evolve independently before they intersect."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1258","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"}