{"paper":{"title":"Ancestries in random $d$-DAGs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Fabian Burghart","submitted_at":"2026-06-29T15:35:46Z","abstract_excerpt":"We consider a random recursive DAG $G_n$ on the vertex set $[n]$ where every vertex $i\\geq 2$ has out-degree $d$, with the targets chosen uniformly at random among the earlier $i-1$ vertices. For this model, we propose a novel way to investigate the descendants of $n$ (which have recently been studied in a paper by Janson) through what we call ancestry processes. The ancestor process $a_i(n)$ of a vertex $i$ is defined as the number of ancestors of $i$ in $G_n$, and is closely related to the evolutions of multi-draw P\\'olya urns. Results on the descendants can then be obtained via asymptotic r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30475","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/2606.30475/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"}