{"id":"https://openalex.org/W7165753261","doi":"https://doi.org/10.48550/arxiv.2606.24465","title":"History estimation in random recursive trees: Pointwise approach via iterated Jordan centralities","display_name":"History estimation in random recursive trees: Pointwise approach via iterated Jordan centralities","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165753261","doi":"https://doi.org/10.48550/arxiv.2606.24465"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2606.24465","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.24465","pdf_url":"https://arxiv.org/pdf/2606.24465","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2606.24465","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018421088","display_name":"Johannes B\u00e4umler","orcid":"https://orcid.org/0000-0002-3823-9899","observed_orcids":["https://orcid.org/0000-0002-3823-9899"]},"institutions":[{"id":"https://openalex.org/I4387153937","display_name":"Universit\u00e4t Koblenz","ror":"https://ror.org/0433e6t24","country_code":"DE","type":"education","lineage":["https://openalex.org/I4387153937"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"B\u00e4umler, Johannes","raw_affiliation_strings":["Mathematical Institute , University of Koblenz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute , University of Koblenz , Germany","institution_ids":["https://openalex.org/I4387153937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078754128","display_name":"Simon Briend","orcid":"https://orcid.org/0009-0009-8655-0532","observed_orcids":["https://orcid.org/0009-0009-8655-0532"]},"institutions":[{"id":"https://openalex.org/I4210134521","display_name":"UniDistance Suisse","ror":"https://ror.org/03exthx58","country_code":"CH","type":"education","lineage":["https://openalex.org/I4210134521"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Briend, Simon","raw_affiliation_strings":["Department of Mathematics and Computer Science , UniDistance , Brig , Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , UniDistance , Brig , Switzerland","institution_ids":["https://openalex.org/I4210134521"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081379847","display_name":"Joost Jorritsma","orcid":"https://orcid.org/0000-0002-1669-9253","observed_orcids":["https://orcid.org/0000-0002-1669-9253"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jorritsma, Joost","raw_affiliation_strings":["Department of Statistics , University of Oxford , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Oxford , United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.8633000254631042,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.8633000254631042,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.04320000112056732,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.01489999983459711,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/random-recursive-trees","display_name":"random recursive trees","score":0.9490000009536743},{"id":"https://openalex.org/keywords/time-of-arrival-estimation","display_name":"time of arrival estimation","score":0.8169999718666077},{"id":"https://openalex.org/keywords/tail-bounds","display_name":"tail bounds","score":0.953000009059906},{"id":"https://openalex.org/keywords/estimation-risk","display_name":"estimation risk","score":0.3919999897480011}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8960000276565552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7192000150680542},{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.7038000226020813},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.569599986076355},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5530999898910522},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5116000175476074},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45570001006126404},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.45329999923706055},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4449000060558319},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4383000135421753},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4277999997138977},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3792000114917755},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3772999942302704},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3750999867916107},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3312000036239624},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33090001344680786},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.3190000057220459},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3059999942779541},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2606.24465","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.24465","pdf_url":"https://arxiv.org/pdf/2606.24465","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2606.24465","doi":"https://doi.org/10.48550/arxiv.2606.24465","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24465","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2606.24465","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.24465","pdf_url":"https://arxiv.org/pdf/2606.24465","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2488694901","display_name":"Mathematical Sciences Research Institute (MSRI)","funder_award_id":"1928930","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G329468232","display_name":null,"funder_award_id":"DMS-1928930","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6019427330","display_name":null,"funder_award_id":"1928930","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311981","display_name":"Magdalen College, University of Oxford","ror":null},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7165753261.pdf","grobid_xml":"https://content.openalex.org/works/W7165753261.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4404995978","https://openalex.org/W7163187576"],"related_works":["https://openalex.org/W4392929657","https://openalex.org/W607912610","https://openalex.org/W7047010833","https://openalex.org/W3037680033","https://openalex.org/W4396815006","https://openalex.org/W2101384922","https://openalex.org/W1982842643","https://openalex.org/W7100858964","https://openalex.org/W2464257288","https://openalex.org/W7155411105"],"abstract_inverted_index":{"We":[0,21,93],"study":[1],"the":[2,6,28,31,44,47,51,57,60,63,73,78,82,104,110,137,143,148,152],"problem":[3],"of":[4,9,30,75,80,106,112,117,151],"estimating":[5],"arrival":[7,65,83],"times":[8],"vertices":[10],"in":[11,42,91,130],"a":[12,23,68,86,95,113,123],"uniform":[13,41],"random":[14],"recursive":[15],"tree":[16,48],"from":[17],"its":[18,156],"unlabeled":[19],"structure.":[20],"adopt":[22],"pointwise":[24],"perspective":[25],"and":[26,35,46,127],"analyze":[27],"distribution":[29],"relative":[32],"estimation":[33,132],"error,":[34],"derive":[36],"tail":[37,101,116],"bounds":[38],"that":[39,59,133],"are":[40],"both":[43],"vertex":[45],"size.":[49],"For":[50],"ranking":[52],"induced":[53],"by":[54,67,85],"Jordan":[55],"centrality,":[56],"probability":[58,79],"estimate":[61],"exceeds":[62],"true":[64],"time":[66,84],"factor":[69,87],"$S$":[70],"decays":[71,89,102],"on":[72,103],"order":[74,105,118,150],"$1/S$,":[76],"while":[77],"underestimating":[81],"$1/S$":[88],"exponentially":[90],"$S$.":[92],"introduce":[94],"refined":[96,144],"centrality":[97,145],"measure":[98,146],"whose":[99],"overestimation":[100],"$(\\log":[107],"S)/S^{2}$,":[108],"at":[109],"cost":[111],"heavier":[114],"lower":[115],"$1/S^{2}$.":[119],"These":[120],"results":[121],"reveal":[122],"tradeoff":[124],"between":[125],"upper-":[126],"lower-tail":[128],"performance":[129],"arrival-time":[131],"is":[134],"invisible":[135],"to":[136],"previously":[138],"studied":[139],"risk":[140,153],"functional.":[141],"Nevertheless,":[142],"attains":[147],"optimal":[149],"for":[154],"all":[155],"parameter":[157],"values.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-06-25T00:00:00"}
