{"id":"https://openalex.org/W4246989326","doi":"https://doi.org/10.1090/fic/012/13","title":"Boolean convolution","display_name":"Boolean convolution","publication_year":1996,"publication_date":"1996-12-10","ids":{"openalex":"https://openalex.org/W4246989326","doi":"https://doi.org/10.1090/fic/012/13"},"language":"en","primary_location":{"id":"doi:10.1090/fic/012/13","doi":"https://doi.org/10.1090/fic/012/13","is_oa":false,"landing_page_url":"https://doi.org/10.1090/fic/012/13","pdf_url":null,"source":{"id":"https://openalex.org/S4306462811","display_name":"American Mathematical Society eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310321506","host_organization_name":"Serbian Mathematical Society","host_organization_lineage":["https://openalex.org/P4310321506"],"host_organization_lineage_names":["Serbian Mathematical Society"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Free Probability Theory","raw_type":"other"},"volume":{"id":"https://openalex.org/W2064052856","display_name":"Free Probability Theory"},"type":"book-chapter","is_traditional":true,"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/A5036407030","display_name":"Roland Speicher","orcid":"https://orcid.org/0000-0002-7986-7496","observed_orcids":["https://orcid.org/0000-0002-7986-7496"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roland Speicher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010087139","display_name":"Reza Woroudi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reza Woroudi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7553,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.87996756,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"267","last_page":"279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.6220999956130981,"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":0.6220999956130981,"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/T13500","display_name":"Probability and Statistical Research","score":0.26170000433921814,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.022700000554323196,"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/boolean-convolution","display_name":"Boolean convolution","score":0.9700000286102295},{"id":"https://openalex.org/keywords/probability-measures","display_name":"probability measures","score":0.847000002861023},{"id":"https://openalex.org/keywords/interval-partitions","display_name":"interval partitions","score":0.9449999928474426},{"id":"https://openalex.org/keywords/free-convolution","display_name":"free convolution","score":0.875},{"id":"https://openalex.org/keywords/non-crossing-partitions","display_name":"noncrossing partitions","score":0.9810000061988831},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"central limit theorem","score":0.9430000185966492},{"id":"https://openalex.org/keywords/poisson-limit-theorem","display_name":"Poisson limit theorem","score":0.9879999756813049},{"id":"https://openalex.org/keywords/infinitely-divisible-distributions","display_name":"infinitely divisible distributions","score":0.9950000047683716},{"id":"https://openalex.org/keywords/stable-distributions","display_name":"stable distributions","score":0.9940000176429749},{"id":"https://openalex.org/keywords/cramer-s-theorem","display_name":"Cram\u00e9r's theorem","score":0.7490000128746033},{"id":"https://openalex.org/keywords/marcinkiewicz-theorem","display_name":"Marcinkiewicz theorem","score":0.871999979019165}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49665409326553345},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.45200297236442566},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36015474796295166},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19002538919448853},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/fic/012/13","doi":"https://doi.org/10.1090/fic/012/13","is_oa":false,"landing_page_url":"https://doi.org/10.1090/fic/012/13","pdf_url":null,"source":{"id":"https://openalex.org/S4306462811","display_name":"American Mathematical Society eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310321506","host_organization_name":"Serbian Mathematical Society","host_organization_lineage":["https://openalex.org/P4310321506"],"host_organization_lineage_names":["Serbian Mathematical Society"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Free Probability Theory","raw_type":"other"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.5996","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.5996","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mast.queensu.ca/~speicher/papers/boolean.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.40.7851","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.7851","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.rzuser.uni-heidelberg.de/~l95/papers/boolean.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2963721385","https://openalex.org/W1557915563","https://openalex.org/W2950454815","https://openalex.org/W7221020796","https://openalex.org/W3126732655","https://openalex.org/W4210882068","https://openalex.org/W3120260095","https://openalex.org/W7095370429","https://openalex.org/W2769895264","https://openalex.org/W7166682452"],"abstract_inverted_index":{"We":[0,52],"introduce":[1],"a":[2],"new":[3],"kind":[4],"of":[5,57,78,82],"convolution":[6,28,42],"for":[7],"probability":[8],"measures.":[9],"This":[10],"`boolean":[11],"convolution'":[12],"is":[13,29,43],"related":[14,30,44],"to":[15,31,45],"interval":[16],"partitions":[17,33,47],"and":[18,34,38,48,64,71,74,85,87],"`partial":[19],"cumulants'":[20],"in":[21],"the":[22,26,35,40,49,58,62,76,79],"same":[23],"way":[24],"as":[25,39],"usual":[27],"all":[32],"classical":[36,80],"cumulants":[37],"free":[41],"non-crossing":[46,50],"cumulants.":[51],"present":[53],"an":[54],"analytic":[55],"description":[56],"boolean":[59],"convolution,":[60],"treat":[61],"central":[63],"Poisson":[65],"limit":[66],"theorems,":[67],"characterize":[68],"infinitely":[69],"divisible":[70],"stable":[72],"distributions":[73],"prove":[75],"analogues":[77],"theorems":[81],"Cram'er,":[83],"Marcinkiewicz,":[84],"Kac":[86],"Loeve.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2022-05-12T00:00:00"}