{"id":"https://openalex.org/W4392560740","doi":"https://doi.org/10.3390/axioms13030173","title":"Some Limiting Laws in Non-Commutative Probability","display_name":"Some Limiting Laws in Non-Commutative Probability","publication_year":2024,"publication_date":"2024-03-07","ids":{"openalex":"https://openalex.org/W4392560740","doi":"https://doi.org/10.3390/axioms13030173"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13030173","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms13030173","pdf_url":"https://www.mdpi.com/2075-1680/13/3/173/pdf?version=1709792876","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/3/173/pdf?version=1709792876","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000311601","display_name":"Ayed R. A. Alanzi","orcid":"https://orcid.org/0000-0002-5337-2276"},"institutions":[{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Ayed. R. A. Alanzi","raw_affiliation_strings":["Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia","Department of mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia","Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia;"],"raw_orcid":"https://orcid.org/0000-0002-5337-2276","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]},{"raw_affiliation_string":"Department of mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia;","institution_ids":["https://openalex.org/I199702508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089048863","display_name":"Raouf Fakhfakh","orcid":"https://orcid.org/0000-0003-2233-4899"},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]},{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]}],"countries":["SA","TN"],"is_corresponding":false,"raw_author_name":"Raouf Fakhfakh","raw_affiliation_strings":["Department of mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia","Laboratory of Probability and Statistics, Faculty of Sciences of Sfax, University of Sfax, Sfax 3029, Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]},{"raw_affiliation_string":"Laboratory of Probability and Statistics, Faculty of Sciences of Sfax, University of Sfax, Sfax 3029, Tunisia","institution_ids":["https://openalex.org/I142899784"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041542650","display_name":"Fatimah Alshahrani","orcid":"https://orcid.org/0000-0003-1306-7688"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fatimah Alshahrani","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia;"],"raw_orcid":"https://orcid.org/0000-0003-1306-7688","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]},{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia;","institution_ids":["https://openalex.org/I106778892"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000311601"],"corresponding_institution_ids":["https://openalex.org/I199702508"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.6458,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66903073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"13","issue":"3","first_page":"173","last_page":"173"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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/T11720","display_name":"Probability and Risk Models","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.7679411172866821},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.6103402972221375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5228160619735718},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4742385745048523},{"id":"https://openalex.org/keywords/law-and-economics","display_name":"Law and economics","score":0.34191781282424927},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.2683558762073517},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.15455463528633118},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.12619075179100037},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1024240255355835}],"concepts":[{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.7679411172866821},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.6103402972221375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5228160619735718},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4742385745048523},{"id":"https://openalex.org/C190253527","wikidata":"https://www.wikidata.org/wiki/Q295354","display_name":"Law and economics","level":1,"score":0.34191781282424927},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.2683558762073517},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15455463528633118},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.12619075179100037},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1024240255355835},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms13030173","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms13030173","pdf_url":"https://www.mdpi.com/2075-1680/13/3/173/pdf?version=1709792876","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b7c91aed8ba3465d9f3f2b04be2f3fe6","is_oa":true,"landing_page_url":"https://doaj.org/article/b7c91aed8ba3465d9f3f2b04be2f3fe6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 3, p 173 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/13/3/173/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13030173","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms13030173","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms13030173","pdf_url":"https://www.mdpi.com/2075-1680/13/3/173/pdf?version=1709792876","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5799999833106995,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G8050936603","display_name":null,"funder_award_id":"PNURSP2024R358","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"}],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392560740.pdf","grobid_xml":"https://content.openalex.org/works/W4392560740.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1985366687","https://openalex.org/W1988344476","https://openalex.org/W1995946241","https://openalex.org/W2021320529","https://openalex.org/W2095712621","https://openalex.org/W2114346036","https://openalex.org/W2610053348","https://openalex.org/W2963009812","https://openalex.org/W2964124055","https://openalex.org/W3016046145","https://openalex.org/W3098442735","https://openalex.org/W3108726781","https://openalex.org/W3179245441","https://openalex.org/W4253567193","https://openalex.org/W4321446955","https://openalex.org/W6829167308"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885","https://openalex.org/W2963966623"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"provide":[4],"some":[5],"new":[6],"limiting":[7,29],"laws":[8,30],"related":[9],"to":[10],"the":[11,34],"free":[12,20],"multiplicative":[13],"law":[14],"of":[15,27,36],"large":[16],"numbers":[17],"and":[18,21],"involving":[19],"Boolean":[22],"additive":[23],"convolutions.":[24],"Some":[25],"examples":[26],"these":[28],"are":[31],"presented":[32],"within":[33],"framework":[35],"non-commutative":[37],"probability":[38],"theory.":[39]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
