{"paper":{"title":"Noise sensitivity and variance lower bound for minimal left-right crossing of a square in first-passage percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Barbara Dembin, Dor Elboim","submitted_at":"2025-05-06T05:58:13Z","abstract_excerpt":"We study first-passage percolation on $\\mathbb Z ^2$ with independent and identically distributed weights, whose common distribution is uniform on $\\{a,b\\}$ with $0<a<b<\\infty $.\n  Following Ahlberg and De la Riva, we consider the passage time $\\tau (n,k)$ of the minimal left-right crossing of the square $[0,n]^2$, whose vertical fluctuations are bounded by $k$. We prove that when $k\\le n^{1/2-\\epsilon}$, the event that $\\tau (n,k)$ is larger than its median is noise sensitive. This improves the main result of Ahlberg and De la Riva which holds when $k\\le n^{1/22-\\epsilon }$.\n  Under the addit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03211","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.03211/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"}