{"paper":{"title":"Coalescence on the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"B\\'ela Bollob\\'as, Bhargav Narayanan, Jonathan Lee, Paul Balister","submitted_at":"2016-10-24T14:34:03Z","abstract_excerpt":"We study a geometrically constrained coalescence model derived from spin systems. Given two probability distributions $\\mathbb{P}_R$ and $\\mathbb{P}_B$ on the positive reals with finite means, colour the real line alternately with red and blue intervals so that the lengths of the red intervals have distribution $\\mathbb{P}_R$, the lengths of the blue intervals have distribution $\\mathbb{P}_B$, and distinct intervals have independent lengths. Now, iteratively update this colouring of the line by coalescing intervals: change the colour of any interval that is surrounded by longer intervals so th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07430","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"}