{"paper":{"title":"Distance between two random k-out digraphs, with and without preferential attachment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Boris Pittel, Nicholas R. Peterson","submitted_at":"2013-11-23T05:04:39Z","abstract_excerpt":"A random k-out mapping (digraph) on [n] is generated by choosing k random images of each vertex one at a time, subject to a \"preferential attachment\" rule: the current vertex selects an image i with probability proportional to a given parameter \\alpha = \\alpha(n) plus the number of times i has already been selected. Intuitively, the larger \\alpha gets, the closer the resulting k-out mapping is to the uniformly random k-out mapping. We prove that \\alpha = \\Theta(n^{1/2}) is the threshold for \\alpha growing \"fast enough\" to make the random digraph approach the uniformly random digraph in terms o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5961","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"}