{"id":"https://openalex.org/W2962795976","doi":"https://doi.org/10.1007/s00493-016-3363-4","title":"Random matrices have simple spectrum","display_name":"Random matrices have simple spectrum","publication_year":2017,"publication_date":"2017-03-24","ids":{"openalex":"https://openalex.org/W2962795976","doi":"https://doi.org/10.1007/s00493-016-3363-4","mag":"2962795976"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-016-3363-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-016-3363-4","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","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/A5066728260","display_name":"Terence Tao","orcid":"https://orcid.org/0000-0002-0140-7641"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Terence Tao","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA, 90095-1555, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA, 90095-1555, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101525096","display_name":"Van Vu","orcid":"https://orcid.org/0009-0000-4473-3992"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Van Vu","raw_affiliation_strings":["Department of Mathematics, Yale University, New Haven, 06520, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yale University, New Haven, 06520, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101525096"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":null,"fwci":5.1258,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.97104066,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"37","issue":"3","first_page":"539","last_page":"553"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":1.0,"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":1.0,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9188311100006104},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8237714767456055},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.7852051854133606},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.662627637386322},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6440969705581665},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.6322692632675171},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6245583295822144},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5711217522621155},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4825296103954315},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.44314852356910706},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.4371187388896942},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3800756335258484},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1468900740146637},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.06651920080184937}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9188311100006104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8237714767456055},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.7852051854133606},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.662627637386322},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6440969705581665},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.6322692632675171},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6245583295822144},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5711217522621155},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4825296103954315},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.44314852356910706},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.4371187388896942},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3800756335258484},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1468900740146637},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.06651920080184937},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-016-3363-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-016-3363-4","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1548847826","https://openalex.org/W1989751882","https://openalex.org/W1994564355","https://openalex.org/W2001765932","https://openalex.org/W2022675369","https://openalex.org/W2081812591","https://openalex.org/W2595959570","https://openalex.org/W2912209775","https://openalex.org/W3083309575","https://openalex.org/W3098671236"],"related_works":["https://openalex.org/W2137261070","https://openalex.org/W1529195008","https://openalex.org/W2070323717","https://openalex.org/W3157489721","https://openalex.org/W38983538","https://openalex.org/W2924468784","https://openalex.org/W2034395027","https://openalex.org/W2034598826","https://openalex.org/W2950949038","https://openalex.org/W2087913063"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
