{"id":"https://openalex.org/W7096835404","doi":null,"title":"The largest eigenvalue of small rank perturbations of Hermitian random matrices, Prob","display_name":"The largest eigenvalue of small rank perturbations of Hermitian random matrices, Prob","publication_year":null,"publication_date":null,"ids":{"openalex":"https://openalex.org/W7096835404"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.583","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.583","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/0411487v1.pdf","raw_type":"text"},"parent_works":[],"lineage":["https://openalex.org/W7096835404"],"child_works_count":0,"type":"preprint","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/A5041211929","display_name":"Sandrine P\u00e9ch\u00e9","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. P\u00e9ch\u00e9","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5041211929"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":9.999999747378752e-05,"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/T11261","display_name":"Quantum chaos and dynamical systems","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":0.9750000238418579},{"id":"https://openalex.org/keywords/hermitian-random-matrices","display_name":"Hermitian random matrices","score":0.9649999737739563},{"id":"https://openalex.org/keywords/gaussian-random-matrices","display_name":"Gaussian random matrices","score":0.6880000233650208},{"id":"https://openalex.org/keywords/edge-of-the-spectrum","display_name":"edge of the spectrum","score":0.7390000224113464},{"id":"https://openalex.org/keywords/large-n-limit","display_name":"large N limit","score":0.5730000138282776}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8985999822616577},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7942000031471252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7580000162124634},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.7548999786376953},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6471999883651733},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.555899977684021},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.532800018787384},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5242999792098999},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49390000104904175},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4812999963760376},{"id":"https://openalex.org/C95707001","wikidata":"https://www.wikidata.org/wiki/Q5121666","display_name":"Circular law","level":5,"score":0.44130000472068787},{"id":"https://openalex.org/C201080289","wikidata":"https://www.wikidata.org/wiki/Q5156587","display_name":"Complex normal distribution","level":3,"score":0.31940001249313354},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.3050000071525574},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.2985000014305115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2935999929904938},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2921000123023987},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.2897999882698059},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.2603999972343445},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.583","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.583","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/0411487v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.8796","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.8796","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/0411487v2.pdf","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/W4394652560","https://openalex.org/W2963514078","https://openalex.org/W4416341002","https://openalex.org/W7099022837","https://openalex.org/W2963873221","https://openalex.org/W7096682735","https://openalex.org/W2164231780","https://openalex.org/W2099551908","https://openalex.org/W2162635298"],"abstract_inverted_index":{"We":[0,26,42],"compute":[1],"the":[2,7,10,19,45,54,64,67],"limiting":[3,59],"eigenvalue":[4,47],"statistics":[5],"at":[6],"edge":[8],"of":[9,12,21,48,66],"spectrum":[11],"large":[13,55],"Hermitian":[14,29],"random":[15,28,50],"matrices":[16,30,51],"perturbed":[17],"by":[18],"addition":[20],"small":[22],"rank":[23,76],"deterministic":[24],"matrices.":[25],"consider":[27],"with":[31,39,82],"independent":[32],"Gaussian":[33],"entries":[34],"Mij,":[35],"i":[36],"\u2264":[37],"j":[38],"various":[40,58],"expectations.":[41],"prove":[43],"that":[44],"largest":[46],"such":[49],"exhibits,":[52],"in":[53,84],"N":[56,70,83],"limit,":[57],"distributions":[60],"depending":[61],"on":[62],"both":[63],"eigenvalues":[65],"matrix":[68],"(EMij)":[69],"i,j=1":[71],"and":[72,90],"its":[73],"rank.":[74],"This":[75],"is":[77],"also":[78],"allowed":[79],"to":[80],"increase":[81],"some":[85],"restricted":[86],"way.":[87],"1":[88],"Introduction":[89]},"counts_by_year":[],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2025-10-27T00:00:00"}
