{"id":"https://openalex.org/W2940546138","doi":"https://doi.org/10.5070/c62156888","title":"A rectangular additive convolution for polynomials","display_name":"A rectangular additive convolution for polynomials","publication_year":2022,"publication_date":"2022-03-29","ids":{"openalex":"https://openalex.org/W2940546138","doi":"https://doi.org/10.5070/c62156888","mag":"2940546138"},"language":"en","primary_location":{"id":"doi:10.5070/c62156888","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c62156888","pdf_url":"https://escholarship.org/content/qt75t2b1bw/qt75t2b1bw.pdf?t=ra2rfs","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt75t2b1bw/qt75t2b1bw.pdf?t=ra2rfs","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018172862","display_name":"Aurelien Gribinski","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Aurelien Gribinski","raw_affiliation_strings":["Princeton University, Princeton, New Jersey, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, New Jersey, U.S.A","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035697843","display_name":"Adam W. Marcus","orcid":"https://orcid.org/0000-0002-3227-903X"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Adam W. Marcus","raw_affiliation_strings":["cole Polytechnique Fdrale de Lausanne (EPFL), Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"cole Polytechnique Fdrale de Lausanne (EPFL), Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018172862"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":0.7116,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59155561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"2","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11716","display_name":"Random Matrices and Applications","score":0.9977999925613403,"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/convolution","display_name":"Convolution (computer science)","score":0.837310791015625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7986721992492676},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.6325165033340454},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.614666223526001},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.5481097102165222},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.547543466091156},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.46015408635139465},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4595045745372772},{"id":"https://openalex.org/keywords/convolution-theorem","display_name":"Convolution theorem","score":0.44628944993019104},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4397240877151489},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.42099520564079285},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41151219606399536},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.38802385330200195},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36384090781211853},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.2209371030330658},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06775981187820435},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.06290709972381592}],"concepts":[{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.837310791015625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7986721992492676},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.6325165033340454},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.614666223526001},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.5481097102165222},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.547543466091156},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.46015408635139465},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4595045745372772},{"id":"https://openalex.org/C79587385","wikidata":"https://www.wikidata.org/wiki/Q2638931","display_name":"Convolution theorem","level":5,"score":0.44628944993019104},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4397240877151489},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.42099520564079285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41151219606399536},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.38802385330200195},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36384090781211853},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.2209371030330658},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06775981187820435},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.06290709972381592},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.5070/c62156888","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c62156888","pdf_url":"https://escholarship.org/content/qt75t2b1bw/qt75t2b1bw.pdf?t=ra2rfs","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1904.11552","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.11552","pdf_url":"https://arxiv.org/pdf/1904.11552","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":"text"},{"id":"mag:2940546138","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1904.11552.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":"pmh:oai:escholarship.org:ark:/13030/qt75t2b1bw","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/75t2b1bw","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorial Theory, vol 2, iss 1","raw_type":"article"},{"id":"pmh:oai:infoscience.epfl.ch:20.500.14299/253694","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/253694","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"research article"},{"id":"doi:10.48550/arxiv.1904.11552","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.11552","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":"doi:10.5070/c62156888","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c62156888","pdf_url":"https://escholarship.org/content/qt75t2b1bw/qt75t2b1bw.pdf?t=ra2rfs","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3794900144","display_name":null,"funder_award_id":"DMS-1552520","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4062780233","display_name":null,"funder_award_id":"1128155","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4894801004","display_name":"CAREER: New Techniques for High Dimensional Systems","funder_award_id":"1552520","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","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/W2940546138.pdf","grobid_xml":"https://content.openalex.org/works/W2940546138.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1664429083","https://openalex.org/W1884490694","https://openalex.org/W1976405176","https://openalex.org/W2051302879","https://openalex.org/W2095087473","https://openalex.org/W2170969870","https://openalex.org/W2222890437","https://openalex.org/W2254643146","https://openalex.org/W2274040325","https://openalex.org/W2552291562","https://openalex.org/W2776898720","https://openalex.org/W2901222675","https://openalex.org/W2949974892","https://openalex.org/W2963034993","https://openalex.org/W3038165843","https://openalex.org/W3103704874","https://openalex.org/W3139555203","https://openalex.org/W6606157326","https://openalex.org/W6637960197","https://openalex.org/W6639666552","https://openalex.org/W6686515201","https://openalex.org/W6760643278"],"related_works":["https://openalex.org/W3016190256","https://openalex.org/W2164645001","https://openalex.org/W2140132297","https://openalex.org/W2911768016","https://openalex.org/W1967297273","https://openalex.org/W1999126428","https://openalex.org/W2170299747","https://openalex.org/W2034349188","https://openalex.org/W126976943","https://openalex.org/W2147690024","https://openalex.org/W2105741817","https://openalex.org/W2990637969","https://openalex.org/W2131446763","https://openalex.org/W152666821"],"abstract_inverted_index":{"Motivated":[0],"by":[1,34,76],"the":[2,15,29,45,49,52,63,71,84,93],"study":[3,14],"of":[4,7,19,48,96,102],"singular":[5],"values":[6],"random":[8],"rectangular":[9,16],"matrices,":[10],"we":[11],"define":[12],"and":[13,37,40],"additive":[17,31],"convolution":[18,32],"polynomials":[20,98],"with":[21,83],"nonnegative":[22],"real":[23],"roots.":[24],"Our":[25],"definition":[26],"directly":[27],"generalizes":[28],"asymmetric":[30],"introduced":[33,75],"Marcus,":[35],"Spielman":[36],"Srivastava":[38],"(2015),":[39],"our":[41],"main":[42,59],"theorem":[43],"gives":[44],"corresponding":[46],"generalization":[47],"bound":[50,91],"on":[51,92],"largest":[53],"root":[54],"from":[55,70],"that":[56],"paper.":[57],"The":[58,79],"tool":[60],"used":[61],"in":[62],"analysis":[64],"is":[65,81],"a":[66,88],"differential":[67],"operator":[68],"derived":[69],"\"rectangular":[72],"Cauchy":[73,94],"transform\"":[74],"Benaych-Georges":[77],"(2009).":[78],"proof":[80],"inductive,":[82],"base":[85],"case":[86],"requiring":[87],"new":[89],"nonasymptotic":[90],"transform":[95],"Gegenbauer":[97],"which":[99],"may":[100],"be":[101],"independent":[103],"interest.Mathematics":[104],"Subject":[105],"Classifications:":[106],"26C10,":[107],"33C45":[108]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}