{"id":"https://openalex.org/W1973290351","doi":"https://doi.org/10.1017/s0963548314000741","title":"Gaussian Distribution of Trie Depth for Strongly Tame Sources","display_name":"Gaussian Distribution of Trie Depth for Strongly Tame Sources","publication_year":2014,"publication_date":"2014-12-11","ids":{"openalex":"https://openalex.org/W1973290351","doi":"https://doi.org/10.1017/s0963548314000741","mag":"1973290351"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548314000741","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000741","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11336/38329","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107305126","display_name":"Eda Cesaratto","orcid":"https://orcid.org/0000-0002-7475-5954"},"institutions":[{"id":"https://openalex.org/I35953669","display_name":"National University of General Sarmiento","ror":"https://ror.org/01k6h2m87","country_code":"AR","type":"education","lineage":["https://openalex.org/I35953669"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"EDA CESARATTO","raw_affiliation_strings":["CONICET and Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, Buenos Aires, Argentina (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CONICET and Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, Buenos Aires, Argentina (e-mail:","institution_ids":["https://openalex.org/I35953669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082150310","display_name":"Brigitte Vall\u00e9e","orcid":"https://orcid.org/0000-0002-2794-6811"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210110254","display_name":"Laboratoire de Physique Corpusculaire de Caen","ror":"https://ror.org/022txr781","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210110254","https://openalex.org/I4210133362","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I4210139483","display_name":"GREYC","ror":"https://ror.org/043749971","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210139483","https://openalex.org/I4210159245","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"BRIGITTE VALL\u00c9E","raw_affiliation_strings":["Laboratoire GREYC, Universit\u00e9 de Caen/ENSICAEN/CNRS, F-14032 Caen, France (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire GREYC, Universit\u00e9 de Caen/ENSICAEN/CNRS, F-14032 Caen, France (e-mail:","institution_ids":["https://openalex.org/I98702875","https://openalex.org/I4210139483","https://openalex.org/I4210110254","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8963,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.68259845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"24","issue":"1","first_page":"54","last_page":"103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.18649999797344208,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.18649999797344208,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.14589999616146088,"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.07769999653100967,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6847529411315918},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6412957906723022},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4984908103942871},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4909515678882599},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.45405298471450806},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3216218650341034},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22957569360733032},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1632491648197174}],"concepts":[{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6847529411315918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6412957906723022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4984908103942871},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4909515678882599},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.45405298471450806},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3216218650341034},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22957569360733032},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1632491648197174},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548314000741","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000741","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01153052v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01153052","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability and Computing, 2015, 24 (01), pp.54-103. ⟨10.1017/S0963548314000741⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-01578305v1","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01578305","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0963-5483","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ri.conicet.gov.ar:11336/38329","is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/38329","pdf_url":null,"source":{"id":"https://openalex.org/S4306401400","display_name":"Conicet","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210104196","host_organization_name":"Centro Cient\u00edfico Tecnol\u00f3gico - Nordeste","host_organization_lineage":["https://openalex.org/I4210104196"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ri.conicet.gov.ar:11336/38329","is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/38329","pdf_url":null,"source":{"id":"https://openalex.org/S4306401400","display_name":"Conicet","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210104196","host_organization_name":"Centro Cient\u00edfico Tecnol\u00f3gico - Nordeste","host_organization_lineage":["https://openalex.org/I4210104196"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W838321193","https://openalex.org/W1582592707","https://openalex.org/W1968884246","https://openalex.org/W1971361861","https://openalex.org/W1971749553","https://openalex.org/W1977905656","https://openalex.org/W1977970493","https://openalex.org/W2005935699","https://openalex.org/W2040409134","https://openalex.org/W2049406057","https://openalex.org/W2053183761","https://openalex.org/W2056364851","https://openalex.org/W2073613132","https://openalex.org/W2079997965","https://openalex.org/W2120393359","https://openalex.org/W2144584558","https://openalex.org/W2160022484","https://openalex.org/W2164247021","https://openalex.org/W2318007796","https://openalex.org/W2485578081","https://openalex.org/W2500470525","https://openalex.org/W6605327614","https://openalex.org/W6671536877"],"related_works":["https://openalex.org/W2952185452","https://openalex.org/W2798106756","https://openalex.org/W1660242800","https://openalex.org/W2046736294","https://openalex.org/W2077211377","https://openalex.org/W2980815195","https://openalex.org/W4293584968","https://openalex.org/W1731719754","https://openalex.org/W2014666842","https://openalex.org/W2036479502"],"abstract_inverted_index":{"The":[0,85,170],"depth":[1,104,288],"of":[2,45,55,73,92,105,113,124,138,162,180,182,201,224,232,278,293],"a":[3,17,24,28,89,106,111,183,194,205,276],"trie":[4,287],"has":[5,79,120,289],"been":[6,82],"deeply":[7],"studied":[8],"when":[9],"the":[10,14,38,41,56,60,71,76,103,118,121,131,134,154,157,160,165,177,198,208,221,229,233,237,253,272,286,290],"source":[11,19,22,29,185],"which":[12,95,187],"produces":[13],"words":[15,114],"is":[16,30,64,143,168,200,226],"simple":[18,31,100,129,269,283,298],"(a":[20],"memoryless":[21,36],"or":[23],"Markov":[25],"chain).":[26],"When":[27],"but":[32],"not":[33,80,97,280],"an":[34,65,144],"unbiased":[35],"source,":[37,57,101,119,284],"expectation":[39,132,155],"and":[40,48,133,141,156,159,248,250],"variance":[42,135],"are":[43,136,149,257],"both":[44,137],"logarithmic":[46,139],"order":[47,140],"their":[49],"dominant":[50],"terms":[51],"involve":[52],"characteristic":[53],"objects":[54],"for":[58,128,153,259,297],"instance":[59],"entropy.":[61],"Moreover,":[62],"there":[63,142],"asymptotic":[66,145,151],"Gaussian":[67,77,146,166,189],"law,":[68],"even":[69,300],"though":[70],"speed":[72,161],"convergence":[74,163],"towards":[75],"law":[78,167,190],"yet":[81],"precisely":[83],"estimated.":[84],"present":[86,273],"paper":[87,171,209,238,274],"describes":[88,275],"\u2018natural\u2019":[90],"class":[91,277],"general":[93,184],"sources,":[94,219,262,299],"does":[96],"contain":[98],"any":[99,282],"where":[102,197,220,285],"random":[107],"trie,":[108],"built":[109],"on":[110,176,211],"set":[112],"independently":[115],"drawn":[116],"from":[117,268],"same":[122,291],"type":[123,292],"probabilistic":[125,294],"behaviour":[126,295],"as":[127,296],"sources:":[130],"law.":[147],"There":[148],"precise":[150,303],"expansions":[152],"variance,":[158],"toward":[164],"optimal.":[169],"first":[172],"provides":[173],"analytical":[174,255],"conditions":[175,256],"Dirichlet":[178,222],"series":[179,199,223],"probabilities":[181,225],"under":[186],"this":[188],"can":[191],"be":[192],"derived:":[193],"pole-free":[195],"region":[196],"polynomial":[202],"growth.":[203],"In":[204],"second":[206],"step,":[207],"focuses":[210],"sources":[212,279],"associated":[213],"with":[214,228,301],"dynamical":[215,218,234,261],"systems,":[216],"called":[217],"expressed":[227],"transfer":[230],"operator":[231],"system.":[235],"Then,":[236],"extends":[239],"results":[240],"due":[241],"to":[242],"Dolgopyat,":[243],"already":[244],"generalized":[245],"by":[246],"Baladi":[247],"Vall\u00e9e,":[249],"shows":[251],"that":[252,264],"previous":[254],"fulfilled":[258],"\u2018most\u2019":[260],"provided":[263],"they":[265],"\u2018strongly":[266],"differ\u2019":[267],"sources.":[270],"Finally,":[271],"containing":[281],"more":[302],"estimates.":[304]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}