{"paper":{"title":"Majority Dynamics on Resampled Sparse Erd\\H{o}s--R\\'enyi Graphs: Gaussian Winner Selection and Pace to Unanimity","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DM","cs.IT","math.CO","math.IT"],"primary_cat":"math.PR","authors_text":"Hai-Xiao Wang, Ioana Dumitriu, Muchen Ju","submitted_at":"2026-08-06T15:28:59Z","abstract_excerpt":"We study the two-opinion majority dynamics process: at each time step, every vertex adopts the majority opinion among its neighbors, retaining its current opinion if there is a tie. Independently at each step, the interaction graph is resampled from the sparse Erd\\H{o}s--R\\'enyi model $\\mathbb G(N,p)$ with $p=b\\log N/N$ and fixed $b>1$.\n  Our results identify three regimes governed by the initial advantage $\\Delta_0=|B_0|-|R_0|$, where $|B_0|$ and $|R_0|$ denote the initial blue and red camps, respectively. First, an initial blue advantage above an explicit constant multiple of $N/\\sqrt{\\log N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06159","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/2608.06159/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"}