{"id":"https://openalex.org/W2000812965","doi":"https://doi.org/10.1017/s0001867800010193","title":"On the LLN for the number of vertices of a random convex hull","display_name":"On the LLN for the number of vertices of a random convex hull","publication_year":2000,"publication_date":"2000-09-01","ids":{"openalex":"https://openalex.org/W2000812965","doi":"https://doi.org/10.1017/s0001867800010193","mag":"2000812965"},"language":"en","primary_location":{"id":"doi:10.1017/s0001867800010193","doi":"https://doi.org/10.1017/s0001867800010193","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0001867800010193","pdf_url":null,"source":{"id":"https://openalex.org/S180803011","display_name":"Advances in Applied Probability","issn_l":"0001-8678","issn":["0001-8678","1475-6064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-c","doyens","jufo-2","norway-2","poland-70","russia-white-list-3","vabb-shw"],"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":"Advances in Applied Probability","raw_type":"journal-article"},"volume":null,"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/A5000528654","display_name":"Bruno Mass\u00e9","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2802487185","display_name":"Universit\u00e9 du littoral c\u00f4te d'opale","ror":"https://ror.org/02gdcg342","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802487185"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Bruno Mass\u00e9","raw_affiliation_strings":["Universit\u00e9 du Littoral C\u00f4te d'Opale"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 du Littoral C\u00f4te d'Opale","institution_ids":["https://openalex.org/I2802487185"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000528654"],"corresponding_institution_ids":["https://openalex.org/I2802487185"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.7184,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.69621384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"32","issue":"03","first_page":"675","last_page":"681"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.004699999932199717,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.002099999925121665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"law of large numbers","score":0.8889999985694885},{"id":"https://openalex.org/keywords/random-convex-hulls","display_name":"random convex hulls","score":0.8500000238418579},{"id":"https://openalex.org/keywords/parent-distribution","display_name":"parent distribution","score":0.6480000019073486},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.8309999704360962},{"id":"https://openalex.org/keywords/random-point-sets","display_name":"random point sets","score":0.46000000834465027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9059971570968628},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7946298718452454},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.687597393989563},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.6841012239456177},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6556333899497986},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5974874496459961},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5100811123847961},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.21828767657279968},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16306334733963013},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15449953079223633},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0001867800010193","doi":"https://doi.org/10.1017/s0001867800010193","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0001867800010193","pdf_url":null,"source":{"id":"https://openalex.org/S180803011","display_name":"Advances in Applied Probability","issn_l":"0001-8678","issn":["0001-8678","1475-6064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-c","doyens","jufo-2","norway-2","poland-70","russia-white-list-3","vabb-shw"],"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":"Advances in Applied Probability","raw_type":"journal-article"},{"id":"doi:10.1239/aap/1013540238","doi":"https://doi.org/10.1239/aap/1013540238","is_oa":false,"landing_page_url":"https://doi.org/10.1239/aap/1013540238","pdf_url":null,"source":{"id":"https://openalex.org/S180803011","display_name":"Advances in Applied Probability","issn_l":"0001-8678","issn":["0001-8678","1475-6064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-c","doyens","jufo-2","norway-2","poland-70","russia-white-list-3","vabb-shw"],"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":"Advances in Applied Probability","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.aap/1013540238","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.aap/1013540238","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6899999976158142}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1256735546","https://openalex.org/W1990434640","https://openalex.org/W2011454249","https://openalex.org/W2024649422","https://openalex.org/W2043395048","https://openalex.org/W2052390545","https://openalex.org/W2067103032","https://openalex.org/W2089261182","https://openalex.org/W2090938461","https://openalex.org/W2091706150","https://openalex.org/W2117218580","https://openalex.org/W2315435126","https://openalex.org/W2319567436","https://openalex.org/W2320682340","https://openalex.org/W2324221193","https://openalex.org/W2326250741","https://openalex.org/W2329645796","https://openalex.org/W2332300174","https://openalex.org/W2465596012"],"related_works":["https://openalex.org/W2467926385","https://openalex.org/W2893068807","https://openalex.org/W161301265","https://openalex.org/W2483619716","https://openalex.org/W4246461909","https://openalex.org/W2377576908","https://openalex.org/W2971424936","https://openalex.org/W2007256320","https://openalex.org/W4226058339","https://openalex.org/W4221156915"],"abstract_inverted_index":{"For":[0],"several":[1],"common":[2],"parent":[3,28],"laws,":[4],"the":[5],"number":[6],"of":[7,9,17,19,26],"vertices":[8],"a":[10,15,27,32],"sample":[11],"convex":[12],"hull":[13],"follows":[14],"kind":[16],"law":[18,29],"large":[20],"numbers.":[21],"We":[22],"exhibit":[23],"an":[24],"example":[25],"which":[30],"contradicts":[31],"general":[33],"conjecture":[34],"about":[35],"this":[36],"matter.":[37]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}
