{"id":"https://openalex.org/W1536448067","doi":"https://doi.org/10.37236/1812","title":"Convergence in Distribution for Subset Counts Between Random Sets","display_name":"Convergence in Distribution for Subset Counts Between Random Sets","publication_year":2004,"publication_date":"2004-09-09","ids":{"openalex":"https://openalex.org/W1536448067","doi":"https://doi.org/10.37236/1812","mag":"1536448067"},"language":"en","primary_location":{"id":"doi:10.37236/1812","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1812","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r59/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r59/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052564891","display_name":"Dudley Stark","orcid":"https://orcid.org/0000-0001-8527-3996"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Dudley Stark","raw_affiliation_strings":["School of Mathematical Sciences Queen Mary, University of London London E1 4NS, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences Queen Mary, University of London London E1 4NS, United Kingdom","institution_ids":["https://openalex.org/I166337079"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052564891"],"corresponding_institution_ids":["https://openalex.org/I166337079"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05850938,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.984499990940094,"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"}},"topics":[{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.984499990940094,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9422000050544739,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.9218999743461609,"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/mathematics","display_name":"Mathematics","score":0.896115779876709},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.7725976705551147},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7512050867080688},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.649718165397644},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5177942514419556},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4908309876918793},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.48777157068252563},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4381817579269409},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.430111825466156},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.42496538162231445},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.38377436995506287},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3105316162109375},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09561720490455627}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.896115779876709},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.7725976705551147},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7512050867080688},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.649718165397644},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5177942514419556},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4908309876918793},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.48777157068252563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4381817579269409},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.430111825466156},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.42496538162231445},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.38377436995506287},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3105316162109375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09561720490455627},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical 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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1812","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1812","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r59/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/1812","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1812","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r59/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1536448067.pdf","grobid_xml":"https://content.openalex.org/works/W1536448067.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2003315074","https://openalex.org/W2022989290","https://openalex.org/W2798655805","https://openalex.org/W4388258552"],"related_works":["https://openalex.org/W2414029657","https://openalex.org/W2917004389","https://openalex.org/W3085309344","https://openalex.org/W150281603","https://openalex.org/W2183541783","https://openalex.org/W138209035","https://openalex.org/W1969020126","https://openalex.org/W1521061676","https://openalex.org/W2384112693","https://openalex.org/W900907376"],"abstract_inverted_index":{"Erd\u0151s":[0],"posed":[1],"the":[2,47,52,58,80],"problem":[3],"of":[4,16,54,82,107,123],"how":[5,114],"many":[6],"random":[7,83],"subsets":[8,84],"need":[9],"to":[10,62,100],"be":[11,101,118],"chosen":[12],"from":[13],"a":[14,88],"set":[15],"$n$":[17],"elements,":[18],"each":[19,23],"element":[20],"appearing":[21],"in":[22,28,37],"subset":[24,34,55,98],"with":[25,69],"probability":[26,49],"$p=1/2$,":[27],"order":[29],"that":[30],"at":[31],"least":[32],"one":[33],"is":[35,72,79],"contained":[36],"another.":[38],"R\u00e9nyi":[39,68],"answered":[40],"this":[41],"question,":[42],"but":[43],"could":[44],"not":[45],"determine":[46],"limiting":[48],"distribution":[50],"for":[51,97,120],"number":[53,81],"counts":[56,99],"because":[57],"higher":[59],"moments":[60],"diverge":[61],"infinity.":[63],"The":[64],"model":[65],"considered":[66],"by":[67,74],"$p$":[70],"arbitrary":[71],"denoted":[73],"${\\cal":[75,124],"P}(m,n,p)$,":[76],"where":[77],"$m$":[78],"chosen.":[85],"We":[86,112],"give":[87],"necessary":[89],"and":[90,95,104],"sufficient":[91],"condition":[92],"on":[93],"$p(n)$":[94],"$m(n)$":[96],"asymptotically":[102],"Poisson":[103,115],"find":[105],"rates":[106],"convergence":[108],"using":[109],"Stein's":[110],"method.":[111],"discuss":[113],"limits":[116],"can":[117],"shown":[119],"other":[121],"statistics":[122],"P}(m,n,p)$.":[125]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
