{"paper":{"title":"Paths with exponential intersection tails and oriented percolation","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Itai Benjamini, Robin Pemantle, Yuval Peres","submitted_at":"1997-01-23T00:00:00Z","abstract_excerpt":"We show that oriented percolation occurs whenever a condition is satisfied called \"exponential intersection tails\". This condition says that a measure on paths exists for which the probability of two independent paths intersecting in more than k sites is exponentially small in k."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9701227","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"}