{"id":"https://openalex.org/W2022718961","doi":"https://doi.org/10.1137/s0097539795283954","title":"Universal Limit Laws for Depths in Random Trees","display_name":"Universal Limit Laws for Depths in Random Trees","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2022718961","doi":"https://doi.org/10.1137/s0097539795283954","mag":"2022718961"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539795283954","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539795283954","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070394029","display_name":"Luc Devroye","orcid":"https://orcid.org/0009-0001-4330-8991"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Luc Devroye","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070394029"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.353,"has_fulltext":false,"cited_by_count":114,"citation_normalized_percentile":{"value":0.89045842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"2","first_page":"409","last_page":"432"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9966999888420105,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9757000207901001,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.8651950359344482},{"id":"https://openalex.org/keywords/random-binary-tree","display_name":"Random binary tree","score":0.7386679649353027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6954505443572998},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6290173530578613},{"id":"https://openalex.org/keywords/weight-balanced-tree","display_name":"Weight-balanced tree","score":0.5982328653335571},{"id":"https://openalex.org/keywords/ternary-search-tree","display_name":"Ternary search tree","score":0.5670307278633118},{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"Law of large numbers","score":0.5580170154571533},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.5552734136581421},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.5339794158935547},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.520566999912262},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5005912780761719},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.49560773372650146},{"id":"https://openalex.org/keywords/optimal-binary-search-tree","display_name":"Optimal binary search tree","score":0.4694654047489166},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4387640655040741},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.43319499492645264},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3335753083229065},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.1890539824962616},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.18624445796012878},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18372589349746704},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15153256058692932},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.1431243121623993},{"id":"https://openalex.org/keywords/interval-tree","display_name":"Interval tree","score":0.12905213236808777},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10571211576461792}],"concepts":[{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.8651950359344482},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.7386679649353027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6954505443572998},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6290173530578613},{"id":"https://openalex.org/C57900377","wikidata":"https://www.wikidata.org/wiki/Q7979855","display_name":"Weight-balanced tree","level":4,"score":0.5982328653335571},{"id":"https://openalex.org/C136519935","wikidata":"https://www.wikidata.org/wiki/Q2859802","display_name":"Ternary search tree","level":5,"score":0.5670307278633118},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.5580170154571533},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.5552734136581421},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.5339794158935547},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.520566999912262},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5005912780761719},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.49560773372650146},{"id":"https://openalex.org/C27628562","wikidata":"https://www.wikidata.org/wiki/Q17154715","display_name":"Optimal binary search tree","level":5,"score":0.4694654047489166},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4387640655040741},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.43319499492645264},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3335753083229065},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.1890539824962616},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.18624445796012878},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18372589349746704},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15153256058692932},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.1431243121623993},{"id":"https://openalex.org/C84927040","wikidata":"https://www.wikidata.org/wiki/Q6057306","display_name":"Interval tree","level":4,"score":0.12905213236808777},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10571211576461792},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0097539795283954","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539795283954","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.2724","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.2724","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-cgrl.cs.mcgill.ca/~luc/devroye_1998_universal_limit_laws_for_depths_in_random_trees.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7200000286102295}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W46381831","https://openalex.org/W194256761","https://openalex.org/W1491528139","https://openalex.org/W1491940285","https://openalex.org/W1500452690","https://openalex.org/W1580085928","https://openalex.org/W1585070348","https://openalex.org/W1590662438","https://openalex.org/W1597637931","https://openalex.org/W1601787207","https://openalex.org/W1649916420","https://openalex.org/W1700611987","https://openalex.org/W1970128728","https://openalex.org/W1971361861","https://openalex.org/W1971711520","https://openalex.org/W1971911733","https://openalex.org/W1976625337","https://openalex.org/W1978606709","https://openalex.org/W1979385638","https://openalex.org/W2000690667","https://openalex.org/W2008048984","https://openalex.org/W2008196645","https://openalex.org/W2009339318","https://openalex.org/W2012069034","https://openalex.org/W2016328747","https://openalex.org/W2018000058","https://openalex.org/W2018795275","https://openalex.org/W2018807466","https://openalex.org/W2018825747","https://openalex.org/W2023135717","https://openalex.org/W2026409183","https://openalex.org/W2028886195","https://openalex.org/W2031292192","https://openalex.org/W2039379906","https://openalex.org/W2042587503","https://openalex.org/W2048858877","https://openalex.org/W2052559705","https://openalex.org/W2052884398","https://openalex.org/W2060242260","https://openalex.org/W2063036437","https://openalex.org/W2067215545","https://openalex.org/W2069347409","https://openalex.org/W2074429597","https://openalex.org/W2086534817","https://openalex.org/W2087284534","https://openalex.org/W2091851562","https://openalex.org/W2093342130","https://openalex.org/W2110042562","https://openalex.org/W2119067845","https://openalex.org/W2125299871","https://openalex.org/W2145929705","https://openalex.org/W2149173084","https://openalex.org/W2152197249","https://openalex.org/W2152828142","https://openalex.org/W2157005274","https://openalex.org/W2168559467","https://openalex.org/W2299950859","https://openalex.org/W2323905269","https://openalex.org/W2337480916","https://openalex.org/W2752853835","https://openalex.org/W2753176400","https://openalex.org/W2913099459","https://openalex.org/W3119264854","https://openalex.org/W4247557894","https://openalex.org/W4247899490"],"related_works":["https://openalex.org/W270522628","https://openalex.org/W2077383771","https://openalex.org/W2146997899","https://openalex.org/W2072157347","https://openalex.org/W2026697457","https://openalex.org/W2013246077","https://openalex.org/W2951678044","https://openalex.org/W2025994050","https://openalex.org/W4300450359","https://openalex.org/W2022718961"],"abstract_inverted_index":{"Random":[0],"binary":[1],"search":[2,5,15],"trees,":[3,6,8,11,26],"b-ary":[4],"median-of-(2k+1)":[7],"quadtrees,":[9],"simplex":[10],"tries,":[12],"and":[13,35],"digital":[14],"trees":[16],"are":[17],"special":[18],"cases":[19],"of":[20,32,42,52],"random":[21],"split":[22],"trees.":[23],"For":[24],"these":[25],"we":[27],"offer":[28],"a":[29,36,50],"universal":[30],"law":[31,38,51],"large":[33,53],"numbers":[34,54],"limit":[37],"for":[39,55],"the":[40,43,56],"depth":[41],"last":[44],"inserted":[45],"point,":[46],"as":[47,49],"well":[48],"height.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}