{"id":"https://openalex.org/W2129741794","doi":"https://doi.org/10.1007/s10208-007-9013-x","title":"The Polynomial Method for Random Matrices","display_name":"The Polynomial Method for Random Matrices","publication_year":2007,"publication_date":"2007-12-12","ids":{"openalex":"https://openalex.org/W2129741794","doi":"https://doi.org/10.1007/s10208-007-9013-x","mag":"2129741794"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-007-9013-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-007-9013-x","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","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/A5113700035","display_name":"N. Raj Rao","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"N. Raj Rao","raw_affiliation_strings":["MIT Department of Electrical Engineering and Computer Science, Cambridge, MA, 02139, USA","MIT Department of Electrical Engineering and Computer Science, 02139, Cambridge, MA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"MIT Department of Electrical Engineering and Computer Science, Cambridge, MA, 02139, USA","institution_ids":[]},{"raw_affiliation_string":"MIT Department of Electrical Engineering and Computer Science, 02139, Cambridge, MA, USA#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029673947","display_name":"Alan Edelman","orcid":"https://orcid.org/0000-0001-7676-3133"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan Edelman","raw_affiliation_strings":["MIT Department of Mathematics, Cambridge, MA, 02139, USA","MIT Department of Mathematics, 02139, Cambridge, MA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"MIT Department of Mathematics, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I4210110987"]},{"raw_affiliation_string":"MIT Department of Mathematics, 02139, Cambridge, MA, USA#TAB#","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113700035"],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.939,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.920994,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"8","issue":"6","first_page":"649","last_page":"702"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9987000226974487,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8171073198318481},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.6010910272598267},{"id":"https://openalex.org/keywords/free-probability","display_name":"Free probability","score":0.5711336731910706},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.45368918776512146},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45030108094215393},{"id":"https://openalex.org/keywords/wishart-distribution","display_name":"Wishart distribution","score":0.43097788095474243},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42733556032180786},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4194377660751343},{"id":"https://openalex.org/keywords/multivariate-random-variable","display_name":"Multivariate random variable","score":0.41331204771995544},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2421606481075287},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17572832107543945}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8171073198318481},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.6010910272598267},{"id":"https://openalex.org/C70120467","wikidata":"https://www.wikidata.org/wiki/Q515893","display_name":"Free probability","level":2,"score":0.5711336731910706},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.45368918776512146},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45030108094215393},{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.43097788095474243},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42733556032180786},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4194377660751343},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.41331204771995544},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2421606481075287},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17572832107543945},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10208-007-9013-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-007-9013-x","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.137.6509","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.6509","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-math.mit.edu/~edelman/homepage/papers/polynomialmethod.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.169.6891","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.169.6891","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mit.edu/%7Eraj/focm_rmt.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.2628","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.2628","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0601389v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.3107","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.3107","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0601389v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.5023","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.5023","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0601389v2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6200000047683716,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W76426102","https://openalex.org/W155856821","https://openalex.org/W591099569","https://openalex.org/W1488435683","https://openalex.org/W1506268158","https://openalex.org/W1517022795","https://openalex.org/W1551177513","https://openalex.org/W1554120007","https://openalex.org/W1572777589","https://openalex.org/W1601581883","https://openalex.org/W1907359947","https://openalex.org/W1969097180","https://openalex.org/W1971210014","https://openalex.org/W1979987326","https://openalex.org/W1995946241","https://openalex.org/W2003189478","https://openalex.org/W2011892826","https://openalex.org/W2021467799","https://openalex.org/W2031246048","https://openalex.org/W2033292040","https://openalex.org/W2039953809","https://openalex.org/W2043905980","https://openalex.org/W2051302879","https://openalex.org/W2054279067","https://openalex.org/W2055791817","https://openalex.org/W2072184935","https://openalex.org/W2074289432","https://openalex.org/W2077522148","https://openalex.org/W2135278638","https://openalex.org/W2170734150","https://openalex.org/W2588543890","https://openalex.org/W2610053348","https://openalex.org/W2802739963","https://openalex.org/W2914659449","https://openalex.org/W2949302343","https://openalex.org/W3098639122","https://openalex.org/W4243997607","https://openalex.org/W4402911082"],"related_works":["https://openalex.org/W2078787338","https://openalex.org/W3101298537","https://openalex.org/W2162274332","https://openalex.org/W3125124522","https://openalex.org/W1991845283","https://openalex.org/W3164104362","https://openalex.org/W2546541196","https://openalex.org/W2765796454","https://openalex.org/W2269779340","https://openalex.org/W3184522547"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}