{"id":"https://openalex.org/W7223136288","doi":"https://doi.org/10.48550/arxiv.2610.27128","title":"Normal approximation for subgraph counts in random intersection graphs: the case of cliques","display_name":"Normal approximation for subgraph counts in random intersection graphs: the case of cliques","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223136288","doi":"https://doi.org/10.48550/arxiv.2610.27128"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.27128","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27128","pdf_url":"https://arxiv.org/pdf/2610.27128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.27128","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002490455","display_name":"Katarzyna Rybarczyk","orcid":"https://orcid.org/0000-0002-3998-6482","observed_orcids":["https://orcid.org/0000-0002-3998-6482"]},"institutions":[{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Rybarczyk, Katarzyna","raw_affiliation_strings":["Faculty of Mathematics and Computer Science , Adam Mickiewicz University , Pozna\u0144 , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science , Adam Mickiewicz University , Pozna\u0144 , Poland","institution_ids":["https://openalex.org/I59411706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058377164","display_name":"Grzegorz Serafin","orcid":"https://orcid.org/0000-0003-3170-6850","observed_orcids":["https://orcid.org/0000-0003-3170-6850"]},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Serafin, Grzegorz","raw_affiliation_strings":["Faculty of Pure and Applied Mathematics , Wroc law University of Science and Technology , Ul. Wybrze\u017ce Wyspia\u0144skiego 27 , Wroc law , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Pure and Applied Mathematics , Wroc law University of Science and Technology , Ul. Wybrze\u017ce Wyspia\u0144skiego 27 , Wroc law , Poland","institution_ids":["https://openalex.org/I11923345"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9667999744415283,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9667999744415283,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.007000000216066837,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.006399999838322401,"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/random-intersection-graphs","display_name":"random intersection graphs","score":0.9940000176429749},{"id":"https://openalex.org/keywords/subgraph-counting","display_name":"subgraph counting","score":0.9269999861717224},{"id":"https://openalex.org/keywords/cliques","display_name":"cliques","score":0.7749999761581421},{"id":"https://openalex.org/keywords/asymptotic-normality","display_name":"asymptotic normality","score":0.902999997138977},{"id":"https://openalex.org/keywords/normal-approximation","display_name":"Gaussian approximation","score":0.7829999923706055},{"id":"https://openalex.org/keywords/kolmogorov-distance","display_name":"Kolmogorov distance","score":0.9070000052452087},{"id":"https://openalex.org/keywords/wasserstein-distance","display_name":"Wasserstein distance","score":0.9900000095367432},{"id":"https://openalex.org/keywords/clique-cover","display_name":"clique cover","score":0.8489999771118164},{"id":"https://openalex.org/keywords/variance-estimation","display_name":"variance estimation","score":0.7400000095367432}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7929999828338623},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.7023000121116638},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.6876000165939331},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6761000156402588},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6575000286102295},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.512499988079071},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5008000135421753},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48539999127388},{"id":"https://openalex.org/C103368685","wikidata":"https://www.wikidata.org/wiki/Q638846","display_name":"Intersection number","level":3,"score":0.4334000051021576},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.4278999865055084},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.2955999970436096},{"id":"https://openalex.org/C189239283","wikidata":"https://www.wikidata.org/wiki/Q17101022","display_name":"Clique graph","level":5,"score":0.2851000130176544},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.27128","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27128","pdf_url":"https://arxiv.org/pdf/2610.27128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.27128","doi":"https://doi.org/10.48550/arxiv.2610.27128","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.27128","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.27128","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27128","pdf_url":"https://arxiv.org/pdf/2610.27128","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223136288.pdf","grobid_xml":"https://content.openalex.org/works/W7223136288.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4417068775","https://openalex.org/W2004262798","https://openalex.org/W2805729591","https://openalex.org/W1998025836","https://openalex.org/W4401147294","https://openalex.org/W2808643311","https://openalex.org/W2990785190","https://openalex.org/W4414984079","https://openalex.org/W204036932","https://openalex.org/W2081943295"],"abstract_inverted_index":{"Let":[0],"$X^{(r)}_n$":[1,33],"denote":[2],"the":[3,13,26,29,35,42,67,72,90],"number":[4],"of":[5,7,32,69,92],"copies":[6],"a":[8,60,86],"complete":[9],"graph":[10,16],"$K_r$":[11],"in":[12,40,89,95],"random":[14,96],"intersection":[15,97],"model":[17],"on":[18,25],"$n$":[19],"vertices.":[20],"We":[21,47],"derive":[22],"upper":[23],"bounds":[24],"distance":[27],"between":[28],"standardized":[30],"version":[31],"and":[34,44,53],"standard":[36],"normal":[37],"distribution,":[38],"measured":[39],"both":[41],"Kolmogorov":[43],"Wasserstein":[45],"metrics.":[46],"complement":[48],"these":[49],"results":[50],"with":[51],"necessary":[52],"sufficient":[54],"conditions":[55],"for":[56,66,79],"asymptotic":[57],"normality.":[58],"As":[59],"byproduct,":[61],"we":[62,74],"provide":[63],"precise":[64],"estimates":[65],"variance":[68],"$X^{(r)}_n$.":[70],"In":[71],"process,":[73],"develop":[75],"new":[76],"general":[77],"techniques":[78],"analysing":[80],"so--called":[81],"clique":[82],"covers,":[83],"which":[84],"play":[85],"crucial":[87],"role":[88],"study":[91],"subgraph":[93],"probabilities":[94],"graphs.":[98]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-22T00:00:00"}