{"id":"https://openalex.org/W2008732718","doi":"https://doi.org/10.1209/0295-5075/78/10001","title":"On the top eigenvalue of heavy-tailed random matrices","display_name":"On the top eigenvalue of heavy-tailed random matrices","publication_year":2007,"publication_date":"2007-03-12","ids":{"openalex":"https://openalex.org/W2008732718","doi":"https://doi.org/10.1209/0295-5075/78/10001","mag":"2008732718"},"language":"en","primary_location":{"id":"doi:10.1209/0295-5075/78/10001","doi":"https://doi.org/10.1209/0295-5075/78/10001","is_oa":false,"landing_page_url":"https://doi.org/10.1209/0295-5075/78/10001","pdf_url":null,"source":{"id":"https://openalex.org/S161185981","display_name":"Europhysics Letters (EPL)","issn_l":"0295-5075","issn":["0295-5075","1286-4854"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Europhysics Letters (EPL)","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cond-mat/0609070","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002294199","display_name":"Giulio Biroli","orcid":"https://orcid.org/0000-0003-4115-2644","observed_orcids":["https://orcid.org/0000-0003-4115-2644"]},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210128565","display_name":"CEA Paris-Saclay","ror":"https://ror.org/03n15ch10","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210128565"]},{"id":"https://openalex.org/I44713367","display_name":"Capital Fund Management (France)","ror":"https://ror.org/01kpwv903","country_code":"FR","type":"company","lineage":["https://openalex.org/I44713367"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G Biroli","raw_affiliation_strings":["Science & Finance, Capital Fund Management - 6 Bd Haussmann, 75009 Paris, France","Service de Physique Th\u00e9orique, Orme des Merisiers, CEA Saclay - 91191 Gif-sur-Yvette Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science & Finance, Capital Fund Management - 6 Bd Haussmann, 75009 Paris, France","institution_ids":["https://openalex.org/I44713367"]},{"raw_affiliation_string":"Service de Physique Th\u00e9orique, Orme des Merisiers, CEA Saclay - 91191 Gif-sur-Yvette Cedex, France","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I4210128565"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083813378","display_name":"Jean\u2010Philippe Bouchaud","orcid":"https://orcid.org/0000-0002-0427-6456","observed_orcids":["https://orcid.org/0000-0002-0427-6456"]},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210115618","display_name":"Service de Physique de l'\u00c9tat Condens\u00e9","ror":"https://ror.org/0247p4w70","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2738703131","https://openalex.org/I4210091594","https://openalex.org/I4210098836","https://openalex.org/I4210113668","https://openalex.org/I4210115618"]},{"id":"https://openalex.org/I4210128565","display_name":"CEA Paris-Saclay","ror":"https://ror.org/03n15ch10","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210128565"]},{"id":"https://openalex.org/I44713367","display_name":"Capital Fund Management (France)","ror":"https://ror.org/01kpwv903","country_code":"FR","type":"company","lineage":["https://openalex.org/I44713367"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J.-P Bouchaud","raw_affiliation_strings":["Science & Finance, Capital Fund Management - 6 Bd Haussmann, 75009 Paris, France","Service de Physique de l'\u00c9tat Condens\u00e9, Orme des Merisiers, CEA Saclay - 91191 Gif-sur-Yvette Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science & Finance, Capital Fund Management - 6 Bd Haussmann, 75009 Paris, France","institution_ids":["https://openalex.org/I44713367"]},{"raw_affiliation_string":"Service de Physique de l'\u00c9tat Condens\u00e9, Orme des Merisiers, CEA Saclay - 91191 Gif-sur-Yvette Cedex, France","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I4210115618","https://openalex.org/I4210128565"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015693419","display_name":"Marc Potters","orcid":"https://orcid.org/0000-0002-6057-7229","observed_orcids":["https://orcid.org/0000-0002-6057-7229"]},"institutions":[{"id":"https://openalex.org/I44713367","display_name":"Capital Fund Management (France)","ror":"https://ror.org/01kpwv903","country_code":"FR","type":"company","lineage":["https://openalex.org/I44713367"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M Potters","raw_affiliation_strings":["Science & Finance, Capital Fund Management - 6 Bd Haussmann, 75009 Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science & Finance, Capital Fund Management - 6 Bd Haussmann, 75009 Paris, France","institution_ids":["https://openalex.org/I44713367"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1895,"currency":"USD","value_usd":1895},"apc_paid":null,"fwci":8.4089,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":{"value":0.97920198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"78","issue":"1","first_page":"10001","last_page":"10001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9994999766349792,"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":0.9994999766349792,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/largest-eigenvalue","display_name":"largest eigenvalue","score":0.9800000190734863},{"id":"https://openalex.org/keywords/power-law-tails","display_name":"power-law tails","score":0.7379999756813049},{"id":"https://openalex.org/keywords/tracy-widom-distribution","display_name":"Tracy-Widom distribution","score":0.9210000038146973},{"id":"https://openalex.org/keywords/frechet-distribution","display_name":"Fr\u00e9chet distribution","score":0.8379999995231628},{"id":"https://openalex.org/keywords/sample-covariance-matrix","display_name":"sample covariance matrix","score":0.9589999914169312},{"id":"https://openalex.org/keywords/extreme-eigenvalues","display_name":"extreme eigenvalues","score":0.8790000081062317},{"id":"https://openalex.org/keywords/finite-size-corrections","display_name":"finite-size corrections","score":0.7129999995231628},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"asymptotic distribution","score":0.3319999873638153}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7907226085662842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7525004148483276},{"id":"https://openalex.org/C95707001","wikidata":"https://www.wikidata.org/wiki/Q5121666","display_name":"Circular law","level":5,"score":0.6287736296653748},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5964248776435852},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.580000102519989},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5425300598144531},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5361452102661133},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4668014645576477},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.44151240587234497},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.43449902534484863},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4339458644390106},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4322613775730133},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.420011043548584},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4154724180698395},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.41363561153411865},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.39273253083229065},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.3247618079185486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20861926674842834},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13166645169258118},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C182514268","wikidata":"https://www.wikidata.org/wiki/Q7636889","display_name":"Sum of normally distributed random variables","level":4,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1209/0295-5075/78/10001","doi":"https://doi.org/10.1209/0295-5075/78/10001","is_oa":false,"landing_page_url":"https://doi.org/10.1209/0295-5075/78/10001","pdf_url":null,"source":{"id":"https://openalex.org/S161185981","display_name":"Europhysics Letters (EPL)","issn_l":"0295-5075","issn":["0295-5075","1286-4854"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Europhysics Letters (EPL)","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:cond-mat/0609070","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0609070","pdf_url":"https://arxiv.org/pdf/cond-mat/0609070","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:edpsciences.org:dkey/10.1209/0295-5075/78/10001","doi":null,"is_oa":false,"landing_page_url":"http://epljournal.edpsciences.org/10.1209/0295-5075/78/10001/pdf","pdf_url":"http://epljournal.edpsciences.org/10.1209/0295-5075/78/10001/pdf","source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1209/0295-5075/78/10001","raw_type":"Text"},{"id":"doi:10.48550/arxiv.cond-mat/0609070","doi":"https://doi.org/10.48550/arxiv.cond-mat/0609070","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.cond-mat/0609070","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cond-mat/0609070","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0609070","pdf_url":"https://arxiv.org/pdf/cond-mat/0609070","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W99142712","https://openalex.org/W187371506","https://openalex.org/W1652609689","https://openalex.org/W1983383403","https://openalex.org/W1992118529","https://openalex.org/W1992446159","https://openalex.org/W1993405207","https://openalex.org/W2017872587","https://openalex.org/W2020001524","https://openalex.org/W2025681266","https://openalex.org/W2060581589","https://openalex.org/W2066459155","https://openalex.org/W2072184935","https://openalex.org/W2090980101","https://openalex.org/W2147573606","https://openalex.org/W2158200899","https://openalex.org/W2161852448","https://openalex.org/W2163997016","https://openalex.org/W2317010637","https://openalex.org/W2499952289","https://openalex.org/W2949734498","https://openalex.org/W2972424502","https://openalex.org/W3100333039","https://openalex.org/W3103343448","https://openalex.org/W3103766153","https://openalex.org/W4229746864","https://openalex.org/W4300546246"],"related_works":["https://openalex.org/W2781869884","https://openalex.org/W1992088950","https://openalex.org/W2765173089","https://openalex.org/W2586623561","https://openalex.org/W2076947890","https://openalex.org/W2010549619","https://openalex.org/W2952374288","https://openalex.org/W2027777023","https://openalex.org/W2033317722","https://openalex.org/W4298860843"],"abstract_inverted_index":{"We":[0,98],"study":[1],"the":[2,5,113,119],"statistics":[3],"of":[4,10,19,53,71,91],"largest":[6,114],"eigenvalue":[7,115],"\u03bb":[8,45,68],"max":[9,46,69],"N":[11,13,22,55,62,73],"\u00d7":[12],"random":[14],"matrices":[15],"with":[16,25,50,59],"IID":[17],"entries":[18],"variance":[20],"1/":[21],",":[23,57],"but":[24,58],"power":[26],"law":[27],"tails":[28],"P":[29],"(":[30],"M":[31,36],"ij":[32,37],")":[33],"\u223c":[34],"|":[35,38],"\u22121\u2212\u03bc":[39],".":[40],"When":[41,64],"\u03bc":[42,65,84],">":[43],"4,":[44,67],"converges":[47],"to":[48,102,116],"2":[49],"Tracy-Widom":[51],"fluctuations":[52],"order":[54,72],"\u22122/3":[56],"large":[60],"finite":[61],"corrections.":[63],"<":[66],"is":[70,76],"2/\u03bc\u22121/2":[74],"and":[75,106],"governed":[77],"by":[78],"Fr\u00e9chet":[79],"statistics.":[80],"The":[81],"marginal":[82],"case":[83],"=":[85],"4":[86],"provides":[87],"a":[88],"new":[89],"class":[90],"limiting":[92],"distribution":[93],"that":[94,108],"we":[95],"compute":[96],"explicitly.":[97],"extend":[99],"these":[100],"results":[101],"sample":[103],"covariance":[104],"matrices,":[105],"show":[107],"extreme":[109],"events":[110],"may":[111],"cause":[112],"significantly":[117],"exceed":[118],"Mar\u010denko-Pastur":[120],"edge.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":11}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}