{"id":"https://openalex.org/W2090357017","doi":"https://doi.org/10.1002/rsa.3240060220","title":"The shape of stretched planar trees","display_name":"The shape of stretched planar trees","publication_year":1995,"publication_date":"1995-03-01","ids":{"openalex":"https://openalex.org/W2090357017","doi":"https://doi.org/10.1002/rsa.3240060220","mag":"2090357017"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240060220","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060220","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures &amp; Algorithms","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/A5069831323","display_name":"Robert S. Maier","orcid":"https://orcid.org/0000-0002-1259-1341"},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert S. Maier","raw_affiliation_strings":["Department of Mathematics, University of Arizona, Tucson, AZ 85721"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Arizona, Tucson, AZ 85721","institution_ids":["https://openalex.org/I138006243"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069831323"],"corresponding_institution_ids":["https://openalex.org/I138006243"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25120148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"2-3","first_page":"331","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9990000128746033,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9990000128746033,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9556000232696533,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9380999803543091,"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/limit","display_name":"Limit (mathematics)","score":0.7935625314712524},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.7850512266159058},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7648025751113892},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.7030137181282043},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5962308645248413},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5837292671203613},{"id":"https://openalex.org/keywords/random-tree","display_name":"Random tree","score":0.5561055541038513},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.5448009371757507},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4336654841899872},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3313865661621094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2566489279270172},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14360836148262024},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1417311131954193},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0669478178024292}],"concepts":[{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7935625314712524},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.7850512266159058},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7648025751113892},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.7030137181282043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5962308645248413},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5837292671203613},{"id":"https://openalex.org/C2776839635","wikidata":"https://www.wikidata.org/wiki/Q14942679","display_name":"Random tree","level":4,"score":0.5561055541038513},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.5448009371757507},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4336654841899872},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3313865661621094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2566489279270172},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14360836148262024},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1417311131954193},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0669478178024292},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.0},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/rsa.3240060220","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060220","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures &amp; Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1980087675","https://openalex.org/W1986187712","https://openalex.org/W2014971447","https://openalex.org/W2048550629","https://openalex.org/W2093891645","https://openalex.org/W2142997539","https://openalex.org/W2145189549","https://openalex.org/W2168559467","https://openalex.org/W2576544140","https://openalex.org/W4229911014","https://openalex.org/W4241638632","https://openalex.org/W4299533062"],"related_works":["https://openalex.org/W2118356379","https://openalex.org/W4385414982","https://openalex.org/W4248554653","https://openalex.org/W4389261498","https://openalex.org/W4297907812","https://openalex.org/W2009934967","https://openalex.org/W2786619496","https://openalex.org/W2563854597","https://openalex.org/W4304892451","https://openalex.org/W4298844991"],"abstract_inverted_index":{"Abstract":[0],"We":[1,68],"study":[2],"the":[3,35,47,54],"asymptotics":[4],"of":[5,9,37,40,49,57],"a":[6,58,65],"\u201cstretched\u201d":[7],"model":[8],"unlabeled":[10],"rooted":[11],"planar":[12],"trees,":[13],"in":[14,62],"which":[15],"trees":[16],"are":[17,22],"not":[18],"taken":[19],"equiprobable":[20],"but":[21],"weighted":[23],"exponentially,":[24],"according":[25],"to":[26,52,64],"their":[27],"height.":[28],"By":[29],"using":[30],"standard":[31],"methods":[32],"for":[33],"computing":[34],"probabilities":[36],"large":[38],"deviations":[39],"random":[41,59],"processes,":[42],"we":[43],"show":[44],"that,":[45],"as":[46],"number":[48],"vertices":[50],"tends":[51],"infinity,":[53],"normalized":[55],"shape":[56],"tree":[60],"converges":[61],"distribution":[63],"deterministic":[66],"limit.":[67],"compute":[69],"this":[70],"limit":[71],"explicitly.":[72],"\u00a9":[73],"1995":[74],"John":[75],"Wiley":[76],"&amp;":[77],"Sons,":[78],"Inc.":[79]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
