{"id":"https://openalex.org/W76426102","doi":null,"title":"FREE PROBABILITY THEORY AND NON-CROSSING PARTITIONS","display_name":"FREE PROBABILITY THEORY AND NON-CROSSING PARTITIONS","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W76426102","mag":"76426102"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.27.9723","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.9723","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://emis.impa.br/journals/SLC/wpapers/s39speicher.ps","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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":true,"raw_author_name":"Roland Speicher","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7986-7496","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5036407030"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4077,"has_fulltext":false,"cited_by_count":93,"citation_normalized_percentile":{"value":0.72090555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"39","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.6366999745368958,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.6366999745368958,"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/T11716","display_name":"Random Matrices and Applications","score":0.1559000015258789,"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":0.13199999928474426,"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/free-probability","display_name":"free probability","score":0.949999988079071},{"id":"https://openalex.org/keywords/non-crossing-partitions","display_name":"noncrossing partitions","score":0.9950000047683716},{"id":"https://openalex.org/keywords/multiplicative-functions","display_name":"multiplicative functions","score":0.8399999737739563},{"id":"https://openalex.org/keywords/freeness","display_name":"freeness","score":0.8489999771118164},{"id":"https://openalex.org/keywords/operator-algebras","display_name":"operator algebras","score":0.734000027179718}],"concepts":[{"id":"https://openalex.org/C70120467","wikidata":"https://www.wikidata.org/wiki/Q515893","display_name":"Free probability","level":2,"score":0.7984777688980103},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7359931468963623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.586736798286438},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5304419994354248},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.522629976272583},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.48183026909828186},{"id":"https://openalex.org/C1975866","wikidata":"https://www.wikidata.org/wiki/Q171448","display_name":"Level crossing","level":2,"score":0.4650033712387085},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4624747037887573},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4415147304534912},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3723919987678528},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08977457880973816},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.27.9723","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.9723","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://emis.impa.br/journals/SLC/wpapers/s39speicher.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.6530","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.6530","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/thurnau.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.5064","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.5064","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/SLC/wpapers/s39speicher.pdf","raw_type":"text"},{"id":"mag:76426102","doi":null,"is_oa":false,"landing_page_url":"https://eudml.org/doc/119380","pdf_url":null,"source":{"id":"https://openalex.org/S4306529545","display_name":"S\u00e9minaire Lotharingien de Combinatoire [electronic only]","issn_l":"1286-4889","issn":["1286-4889"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","poland-20","russia-white-list-4"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"S\u00e9minaire Lotharingien de Combinatoire [electronic only]","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1599997798","https://openalex.org/W1613083486","https://openalex.org/W1708958458","https://openalex.org/W1970765130","https://openalex.org/W1972912363","https://openalex.org/W1983413858","https://openalex.org/W1990854005","https://openalex.org/W1995946241","https://openalex.org/W1999106065","https://openalex.org/W2007700378","https://openalex.org/W2020518828","https://openalex.org/W2021798854","https://openalex.org/W2029272161","https://openalex.org/W2032690805","https://openalex.org/W2040661328","https://openalex.org/W2051302879","https://openalex.org/W2063211788","https://openalex.org/W2064052856","https://openalex.org/W2078206885","https://openalex.org/W2078582032","https://openalex.org/W2087543605","https://openalex.org/W2095712621","https://openalex.org/W2610053348","https://openalex.org/W2887306455"],"related_works":["https://openalex.org/W2115107777","https://openalex.org/W7095121584","https://openalex.org/W3139190418","https://openalex.org/W7100095014","https://openalex.org/W2002490441","https://openalex.org/W2485493998","https://openalex.org/W1921063444","https://openalex.org/W2087543605","https://openalex.org/W7095958285","https://openalex.org/W1990854005"],"abstract_inverted_index":{".":[0],"Voiculescu's":[1],"free":[2,70],"probability":[3,71],"theory":[4,22,72,97],"--":[5,31,63],"which":[6],"was":[7,83],"introduced":[8,84],"in":[9,89,95,134],"an":[10,20,33,138,148],"operator":[11,99],"algebraic":[12],"context,":[13],"but":[14,147],"has":[15,32],"since":[16],"then":[17],"developed":[18],"into":[19],"exciting":[21],"with":[23,91],"a":[24,113],"lot":[25],"of":[26,45,51,81,98,129,140],"links":[27],"to":[28,59,117],"other":[29],"fields":[30],"interesting":[34],"combinatorial":[35,43],"facet:":[36],"it":[37,111],"can":[38],"be":[39,118],"described":[40],"by":[41,85],"the":[42,49,96,127,141],"concept":[44,114,144],"multiplicative":[46],"functions":[47],"on":[48,69,74,120],"lattice":[50],"non-crossing":[52,75],"partitions.":[53,76],"In":[54],"this":[55,61,106],"survey":[56],"I":[57],"want":[58],"explain":[60],"connection":[62,90],"without":[64],"assuming":[65],"any":[66],"knowledge":[67],"neither":[68],"nor":[73],"1.":[77],"Introduction":[78],"The":[79],"notion":[80],"`freeness'":[82],"Voiculescu":[86,102],"around":[87],"1985":[88],"some":[92,135],"old":[93],"questions":[94],"algebras.":[100],"But":[101],"separated":[103],"freeness":[104,132],"from":[105],"special":[107],"context":[108],"and":[109],"emphasized":[110],"as":[112],"being":[115],"worth":[116],"investigated":[119],"its":[121],"own":[122],"sake.":[123],"Furthermore,":[124],"he":[125],"advocated":[126],"point":[128],"view":[130],"that":[131],"behaves":[133],"respects":[136],"like":[137],"analogue":[139,149],"classical":[142],"probabilistic":[143],"`independence'":[145],"-":[146],"for":[150],"non-commutative":[151],"rando...":[152]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}