{"paper":{"title":"Bootstrap percolation in power-law random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CO"],"primary_cat":"math.PR","authors_text":"Hamed Amini, Nikolaos Fountoulakis","submitted_at":"2011-11-05T18:40:49Z","abstract_excerpt":"A bootstrap percolation process on a graph $G$ is an \"infection\" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours becomes infected and remains so forever. The parameter $r\\geq 2$ is fixed. Such processes have been used as models for the spread of ideas or trends within a network of individuals.\n  We analyse bootstrap percolation process in the case where the underlying graph is an inhomogeneous random graph, which exhibits a power-law degree distribution, and initially th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1339","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"}