{"paper":{"title":"The contact process on the complete graph with random vertex-dependent infection rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathon Peterson","submitted_at":"2010-05-05T18:52:05Z","abstract_excerpt":"We study the contact process on the complete graph on $n$ vertices where the rate at which the infection travels along the edge connecting vertices $i$ and $j$ is equal to $ \\lambda w_i w_j / n$ for some $\\lambda >0$, where $w_i$ are i.i.d. vertex weights. We show that when $E[w_1^2] < \\infty$ there is a phase transition at $\\lambda_c > 0$ so that for $\\lambda<\\lambda_c$ the contact process dies out in logarithmic time, and for $\\lambda>\\lambda_c$ the contact process lives for an exponential amount of time. Moreover, we give a formula for $\\lambda_c$ and when $\\lambda>\\lambda_c$ we are able to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0810","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"}