{"id":"https://openalex.org/W4200491576","doi":"https://doi.org/10.1080/10586458.2021.2011806","title":"Evidence of Random Matrix Corrections for the Large Deviations of Selberg\u2019s Central Limit Theorem","display_name":"Evidence of Random Matrix Corrections for the Large Deviations of Selberg\u2019s Central Limit Theorem","publication_year":2021,"publication_date":"2021-12-20","ids":{"openalex":"https://openalex.org/W4200491576","doi":"https://doi.org/10.1080/10586458.2021.2011806"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2021.2011806","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2021.2011806","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental 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/A5070142343","display_name":"Eli Amzallag","orcid":null},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. Amzallag","raw_affiliation_strings":["Department of Mathematics, City College of New York, CUNY, New York, USA;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City College of New York, CUNY, New York, USA;","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046144341","display_name":"Louis\u2010Pierre Arguin","orcid":"https://orcid.org/0000-0003-4704-2622"},"institutions":[{"id":"https://openalex.org/I121847817","display_name":"The Graduate Center, CUNY","ror":"https://ror.org/00awd9g61","country_code":"US","type":"education","lineage":["https://openalex.org/I121847817"]},{"id":"https://openalex.org/I141810926","display_name":"Baruch College","ror":"https://ror.org/023qavy03","country_code":"US","type":"education","lineage":["https://openalex.org/I141810926"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"L.-P. Arguin","raw_affiliation_strings":["Department of Mathematics, Baruch College, CUNY, New York, USA;","Department of Mathematics, CUNY Graduate Center, New York, USA;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Baruch College, CUNY, New York, USA;","institution_ids":["https://openalex.org/I141810926"]},{"raw_affiliation_string":"Department of Mathematics, CUNY Graduate Center, New York, USA;","institution_ids":["https://openalex.org/I121847817"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057956010","display_name":"Emma Bailey","orcid":"https://orcid.org/0000-0003-3558-1602"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]},{"id":"https://openalex.org/I121847817","display_name":"The Graduate Center, CUNY","ror":"https://ror.org/00awd9g61","country_code":"US","type":"education","lineage":["https://openalex.org/I121847817"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"E. Bailey","raw_affiliation_strings":["Department of Mathematics, CUNY Graduate Center, New York, USA;","Department of Mathematics, University of Bristol, Bristol, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, CUNY Graduate Center, New York, USA;","institution_ids":["https://openalex.org/I121847817"]},{"raw_affiliation_string":"Department of Mathematics, University of Bristol, Bristol, UK","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028964136","display_name":"Ka-Hei Hui","orcid":"https://orcid.org/0000-0002-9786-2648"},"institutions":[{"id":"https://openalex.org/I141810926","display_name":"Baruch College","ror":"https://ror.org/023qavy03","country_code":"US","type":"education","lineage":["https://openalex.org/I141810926"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. Hui","raw_affiliation_strings":["Department of Mathematics, Baruch College, CUNY, New York, USA;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Baruch College, CUNY, New York, USA;","institution_ids":["https://openalex.org/I141810926"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045666117","display_name":"R. Rama Chandra Rao","orcid":null},"institutions":[{"id":"https://openalex.org/I141810926","display_name":"Baruch College","ror":"https://ror.org/023qavy03","country_code":"US","type":"education","lineage":["https://openalex.org/I141810926"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Rao","raw_affiliation_strings":["Department of Mathematics, Baruch College, CUNY, New York, USA;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Baruch College, CUNY, New York, USA;","institution_ids":["https://openalex.org/I141810926"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5046144341"],"corresponding_institution_ids":["https://openalex.org/I121847817","https://openalex.org/I141810926"],"apc_list":null,"apc_paid":null,"fwci":2.4566,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.89306122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"33","issue":"1","first_page":"123","last_page":"135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11166","display_name":"Analytic Number Theory Research","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.9983999729156494,"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/mathematics","display_name":"Mathematics","score":0.9013432264328003},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.7559767961502075},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5401654839515686},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5306020379066467},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5156897306442261},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5040263533592224},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.48532217741012573},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.47620925307273865},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4603787064552307},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4286196827888489},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4176423251628876},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4143407940864563},{"id":"https://openalex.org/keywords/second-moment-of-area","display_name":"Second moment of area","score":0.4106401801109314},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3320903778076172},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20678454637527466},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13613417744636536},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09296098351478577}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9013432264328003},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.7559767961502075},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5401654839515686},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5306020379066467},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5156897306442261},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5040263533592224},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.48532217741012573},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.47620925307273865},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4603787064552307},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4286196827888489},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4176423251628876},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4143407940864563},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.4106401801109314},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3320903778076172},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20678454637527466},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13613417744636536},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09296098351478577},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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":1,"locations":[{"id":"doi:10.1080/10586458.2021.2011806","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2021.2011806","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6109274828","display_name":null,"funder_award_id":"DMS-1653602","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1535638438","https://openalex.org/W1873500983","https://openalex.org/W1967457180","https://openalex.org/W1986075005","https://openalex.org/W1986386529","https://openalex.org/W1986417812","https://openalex.org/W2013205609","https://openalex.org/W2018340063","https://openalex.org/W2056183459","https://openalex.org/W2058590036","https://openalex.org/W2095393613","https://openalex.org/W2101367141","https://openalex.org/W2106226212","https://openalex.org/W2110599431","https://openalex.org/W2134478378","https://openalex.org/W2169254136","https://openalex.org/W2332902263","https://openalex.org/W2491331606","https://openalex.org/W2499078703","https://openalex.org/W2591008310","https://openalex.org/W2962707111","https://openalex.org/W2962755272","https://openalex.org/W2962996535","https://openalex.org/W2963237125","https://openalex.org/W2976790204","https://openalex.org/W3101668086","https://openalex.org/W3101974007","https://openalex.org/W3102962433","https://openalex.org/W3121187802","https://openalex.org/W3126947126","https://openalex.org/W6775989732"],"related_works":["https://openalex.org/W2325559318","https://openalex.org/W4231167465","https://openalex.org/W650906410","https://openalex.org/W4246456327","https://openalex.org/W1890075812","https://openalex.org/W4251533179","https://openalex.org/W1908930887","https://openalex.org/W1825355621","https://openalex.org/W2032023312","https://openalex.org/W4211266680"],"abstract_inverted_index":{"Selberg\u2019s":[0],"central":[1,162],"limit":[2,163],"theorem":[3,164],"states":[4],"that":[5,42,109],"the":[6,75,78,86,90,117,120,136,139,156,160,166,169],"values":[7,48],"of":[8,28,49,89,93,119,122,127,135,142,148,159,168,172],"log":[9,35,51,52,65,66,123,130],"|\u03b6(1/2+i\u03c4)|,":[10],"where":[11,54],"\u03c4":[12],"is":[13],"a":[14,24,55,113,173],"uniform":[15],"random":[16,26,174],"variable":[17,27],"on":[18,116],"[T,2T],":[19],"are":[20],"asymptotically":[21],"distributed":[22],"like":[23],"Gaussian":[25],"mean":[29],"0":[30],"and":[31,83,101,183],"standard":[32],"deviation":[33],"12log":[34],"T.":[36],"It":[37],"was":[38],"conjectured":[39,80],"by":[40,81,180],"Radziwi\u0142\u0142":[41],"this":[43,96,105,110],"distribution":[44,118],"breaks":[45],"down":[46],"for":[47,85,104,145,165],"order":[50,149],"T,":[53,67],"multiplicative":[56],"correction":[57,111,153],"Ck":[58,143],"would":[59],"be":[60,74],"present":[61],"at":[62],"level":[63],"k":[64,68],">":[69],"0.":[70],"This":[71],"constant":[72],"should":[73],"same":[76],"as":[77,177],"one":[79],"Keating":[82],"Snaith":[84],"leading":[87],"asymptotic":[88],"2kth":[91],"moment":[92],"\u03b6.":[94],"In":[95],"paper,":[97],"we":[98],"provide":[99],"numerical":[100,140],"theoretical":[102],"evidence":[103],"conjecture.":[106],"We":[107],"propose":[108],"has":[112],"significant":[114],"effect":[115],"maximum":[121],"|\u03b6|":[124],"in":[125,155],"intervals":[126],"size":[128],"(":[129],"T)\u03b8,":[131],"\u03b8>0.":[132],"The":[133],"precision":[134],"prediction":[137],"enables":[138],"detection":[141],"even":[144],"low":[146],"T\u2019s":[147],"T=108.":[150],"A":[151],"similar":[152],"appears":[154],"large":[157],"deviations":[158],"Keating\u2013Snaith":[161],"logarithm":[167],"characteristic":[170],"polynomial":[171],"unitary":[175],"matrix,":[176],"first":[178],"proved":[179],"F\u00e9ray,":[181],"M\u00e9liot":[182],"Nikeghbali.":[184]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}