{"paper":{"title":"One-arm domination time in Cylindrical Hastings-Levitov$(0)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eviatar B. Procaccia, Guanyi Chen, Yuxuan Zong","submitted_at":"2025-07-15T06:49:35Z","abstract_excerpt":"The cylindrical Hastings-Levitov$(0)$ admits a single infinite connected tree (arm). For a cylinder of width $N$ and particles of size $\\lambda$, {we consider the first time $\\upsilon_{N, \\lambda}$ after which only the unique infinite tree receives particles}. We prove that $\\frac{cN^2}{\\lambda^3} \\le \\mathbb{E}[\\upsilon_{N, \\lambda}]\\le\\frac{CN^2}{\\lambda^3}$, and establish an exponential tail for $\\upsilon_{N, \\lambda}$. Moreover, we obtain an asymptotic bound to the expected total number of trees, and the last time a new tree emerges."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11028","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.11028/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}