{"paper":{"title":"Majority bootstrap percolation on the random graph G(n,p)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sigurdur \\\"Orn Stef\\'ansson, Thomas Vallier","submitted_at":"2015-03-24T13:31:27Z","abstract_excerpt":"Majority bootstrap percolation on the random graph $G_{n,p}$ is a process of spread of \"activation\" on a given realisation of the graph with a given number of initially active nodes. At each step those vertices which have more active neighbours than inactive neighbours become active as well.\n  We study the size $A^*$ of the final active set. The parameters of the model are, besides $n$ (tending to $\\infty$), the size $A(0)=A_0(n)$ of the initially active set and the probability $p=p(n)$ of the edges in the graph. We prove that the process cannot percolate for $A(0) = o(n)$. We study the proces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07029","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"}