{"paper":{"title":"Infinite collisions of simple random walks on random recursive trees generated by Bernoulli sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng Wang, Jia-shan Tang, Xian-Yuan Wu","submitted_at":"2026-07-03T03:23:17Z","abstract_excerpt":"In this paper, we study random recursive trees generated by Bernoulli sequences. Starting from a graph with two vertices and one edge, each new vertex is connected to the last vertex with probability $ p $, or to the second-last vertex with probability $ q = 1-p $, this recursive construction yields a random infinite recursive tree $T$. We prove that $T$ almost surely has exactly one topological end. Furthermore, we establish that $T$ has the infinite collision property: two independent simple random walks on $T$ collide infinitely often almost surely."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02916","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/2607.02916/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"}