{"id":"https://openalex.org/W2786337572","doi":"https://doi.org/10.1017/s0963548319000348","title":"Surjectivity of near-square random matrices","display_name":"Surjectivity of near-square random matrices","publication_year":2019,"publication_date":"2019-11-06","ids":{"openalex":"https://openalex.org/W2786337572","doi":"https://doi.org/10.1017/s0963548319000348","mag":"2786337572"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548319000348","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548319000348","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1802.00001","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049907101","display_name":"Hoi H. Nguyen","orcid":"https://orcid.org/0000-0002-4590-9301"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hoi. H. Nguyen","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH43210, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH43210, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041511721","display_name":"Elliot Paquette","orcid":"https://orcid.org/0000-0003-4156-6687"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elliot Paquette","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH43210, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH43210, USA","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049907101"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00977678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"2","first_page":"267","last_page":"292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9984999895095825,"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":0.7059293985366821},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.6606783866882324},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.5927096605300903},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.5817498564720154},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5749551057815552},{"id":"https://openalex.org/keywords/square-lattice","display_name":"Square lattice","score":0.5478656888008118},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4697188436985016},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.46408602595329285},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.4441574215888977},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4268070459365845},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3320956826210022},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.31499719619750977},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15189236402511597},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.12322396039962769},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08648735284805298},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06277340650558472},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.04377657175064087},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0435175895690918}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7059293985366821},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.6606783866882324},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.5927096605300903},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.5817498564720154},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5749551057815552},{"id":"https://openalex.org/C2777620828","wikidata":"https://www.wikidata.org/wiki/Q7582067","display_name":"Square lattice","level":3,"score":0.5478656888008118},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4697188436985016},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.46408602595329285},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.4441574215888977},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4268070459365845},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3320956826210022},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.31499719619750977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15189236402511597},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.12322396039962769},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08648735284805298},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06277340650558472},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.04377657175064087},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0435175895690918},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548319000348","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548319000348","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1802.00001","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.00001","pdf_url":"https://arxiv.org/pdf/1802.00001","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":null},{"id":"mag:2786337572","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1802.00001.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1802.00001","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.00001","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1802.00001","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.00001","pdf_url":"https://arxiv.org/pdf/1802.00001","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2786337572.pdf","grobid_xml":"https://content.openalex.org/works/W2786337572.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1830907302","https://openalex.org/W1914271854","https://openalex.org/W1955801390","https://openalex.org/W1973590672","https://openalex.org/W1995416687","https://openalex.org/W2009136691","https://openalex.org/W2047705353","https://openalex.org/W2066513831","https://openalex.org/W2081131431","https://openalex.org/W2162994716","https://openalex.org/W2810977476","https://openalex.org/W2912209775","https://openalex.org/W2914659449","https://openalex.org/W2963301182","https://openalex.org/W2963541360","https://openalex.org/W2963631045","https://openalex.org/W2997974598","https://openalex.org/W6667279045"],"related_works":["https://openalex.org/W2805298288","https://openalex.org/W3090168662","https://openalex.org/W2766602316","https://openalex.org/W2010549619","https://openalex.org/W1717654527","https://openalex.org/W3104655732","https://openalex.org/W2804984011","https://openalex.org/W71577644","https://openalex.org/W2934361511","https://openalex.org/W2617226643","https://openalex.org/W1999370902","https://openalex.org/W2953174700","https://openalex.org/W2138347828","https://openalex.org/W2955957831","https://openalex.org/W3106698896","https://openalex.org/W2895594478","https://openalex.org/W2042765770","https://openalex.org/W2076944648","https://openalex.org/W1994231597","https://openalex.org/W2371392029"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"show":[2],"that":[3],"a":[4,26],"nearly":[5],"square":[6],"independent":[7],"and":[8],"identically":[9],"distributed":[10],"random":[11],"integral":[12,18],"matrix":[13],"is":[14],"surjective":[15],"over":[16],"the":[17],"lattice":[19],"with":[20],"very":[21],"high":[22],"probability.":[23],"This":[24],"answers":[25],"question":[27],"by":[28],"Koplewitz":[29],"[6].":[30],"Our":[31],"result":[32],"extends":[33],"to":[34,40],"sparse":[35],"matrices":[36,41],"as":[37,39],"well":[38],"of":[42],"dependent":[43],"entries.":[44]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}