{"paper":{"title":"Short survey of results and open problems for parking problems on random trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrej Srakar","submitted_at":"2025-05-13T12:28:41Z","abstract_excerpt":"Parking problems derive from works in combinatorics by Konheim and Weiss in the 1960s. In a memorable contribution, Lackner and Panholzer (2016) studied parking on a random tree and established a phase transition for this process when \\(m \\approx \\frac{n}{2}\\). This relates to the renowned result by David Aldous of convergence results on Erd\\H{o}s-Renyi random graphs of order \\(n^{\\frac{2}{3}}\\). In a series of recent articles, Contat and coauthors have studied the problem in various random tree contexts and derived several novel scaling limit and phase transition results. We survey the presen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15826","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/2505.15826/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"}