{"id":"https://openalex.org/W7220730786","doi":"https://doi.org/10.48550/arxiv.2610.06785","title":"On the Growth Factor of Random Matrices","display_name":"On the Growth Factor of Random Matrices","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220730786","doi":"https://doi.org/10.48550/arxiv.2610.06785"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06785","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06785","pdf_url":"https://arxiv.org/pdf/2610.06785","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.06785","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056576989","display_name":"John Urschel","orcid":"https://orcid.org/0000-0002-5401-821X","observed_orcids":["https://orcid.org/0000-0002-5401-821X"]},"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"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Urschel, John","raw_affiliation_strings":["Department of Mathematics , Massachusetts Institute of Technology , Cambridge , MA , 02139 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Massachusetts Institute of Technology , Cambridge , MA , 02139 USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056576989"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/growth-factors","display_name":"growth factors","score":0.9369999766349792},{"id":"https://openalex.org/keywords/random-matrices","display_name":"random matrices","score":0.9350000023841858},{"id":"https://openalex.org/keywords/gaussian-matrices","display_name":"Gaussian matrices","score":0.8450000286102295},{"id":"https://openalex.org/keywords/partial-pivoting","display_name":"partial pivoting","score":0.9039999842643738},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"numerical stability","score":0.7730000019073486},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.9359999895095825},{"id":"https://openalex.org/keywords/smoothed-analysis","display_name":"smoothed analysis","score":0.6420000195503235},{"id":"https://openalex.org/keywords/preconditioning","display_name":"preconditioning","score":0.5979999899864197},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"asymptotic distribution","score":0.9039999842643738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8109999895095825},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6482999920845032},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5916000008583069},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5450000166893005},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5277000069618225},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.43639999628067017},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41690000891685486},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3991999924182892},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.36000001430511475},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.3497999906539917},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.32499998807907104},{"id":"https://openalex.org/C175380299","wikidata":"https://www.wikidata.org/wiki/Q6852339","display_name":"Normal matrix","level":3,"score":0.30869999527931213},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3003999888896942},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2736999988555908},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.26409998536109924}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06785","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06785","pdf_url":"https://arxiv.org/pdf/2610.06785","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":"doi:10.48550/arxiv.2610.06785","doi":"https://doi.org/10.48550/arxiv.2610.06785","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06785","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.06785","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06785","pdf_url":"https://arxiv.org/pdf/2610.06785","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3219000786","display_name":"Estimating Eigenvalues and Matrix Functions with a Krylov Subspace","funder_award_id":"2513687","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220730786.pdf","grobid_xml":"https://content.openalex.org/works/W7220730786.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7202172875","https://openalex.org/W7203927659"],"related_works":["https://openalex.org/W7203927659","https://openalex.org/W2170078634","https://openalex.org/W7220957172","https://openalex.org/W7220659047","https://openalex.org/W2108029014","https://openalex.org/W4401767635","https://openalex.org/W2115780241","https://openalex.org/W2141900211","https://openalex.org/W2165917639","https://openalex.org/W4395000858"],"abstract_inverted_index":{"Gaussian":[0,84,103],"elimination":[1],"is":[2,21,108],"the":[3,24,48,60,76,80,95,136],"oldest":[4],"and":[5,74,89],"most":[6,90],"popular":[7],"method":[8],"for":[9,17,59],"solving":[10],"a":[11,18,27,42,64,68],"linear":[12],"system.":[13],"Its":[14],"numerical":[15],"stability":[16],"given":[19],"matrix":[20,65,71,104],"controlled":[22],"by":[23,67],"growth":[25,49,61,81,96,137],"factor,":[26],"measure":[28],"of":[29,44,51,63,79,83,98,118,135],"how":[30],"large":[31],"entries":[32],"can":[33],"become":[34],"during":[35],"elimination.":[36],"In":[37],"this":[38,127],"work,":[39],"we":[40,55,92],"prove":[41,93,126],"number":[43],"new":[45],"results":[46],"regarding":[47],"factor":[50,62,82,97,138],"random":[52],"matrices.":[53],"First,":[54],"provide":[56,130],"tight":[57],"estimates":[58],"preconditioned":[66],"Haar":[69],"orthogonal":[70],"without":[72,86],"pivoting":[73,107],"characterize":[75],"asymptotic":[77],"distribution":[78],"matrices":[85],"pivoting.":[87,141],"Second,":[88],"notably,":[91],"that":[94],"an":[99,115,131],"$n":[100],"\\times":[101],"n$":[102],"under":[105,139],"partial":[106,140],"rarely":[109],"much":[110],"larger":[111],"than":[112],"$\\sqrt{n}$,":[113],"resolving":[114],"old":[116],"conjecture":[117,128],"Nick":[119],"Trefethen.":[120],"The":[121],"same":[122],"techniques":[123],"used":[124],"to":[125],"also":[129],"improved":[132],"smoothed":[133],"analysis":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
