{"id":"https://openalex.org/W4410927317","doi":"https://doi.org/10.4086/toc.2025.v021a001","title":"","display_name":"","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4410927317","doi":"https://doi.org/10.4086/toc.2025.v021a001"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2025.v021a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2025.v021a001","pdf_url":"https://theoryofcomputing.org/articles/v021a001/v021a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v021a001/v021a001.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100599394","display_name":"Yinan Li","orcid":"https://orcid.org/0000-0001-7137-7823"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yinan Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100948185","display_name":"Youming Qiao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Youming Qiao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039043184","display_name":"Avi Wigderson","orcid":"https://orcid.org/0000-0002-1539-1417"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avi Wigderson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042083332","display_name":"Yuval Wigderson","orcid":"https://orcid.org/0000-0001-5909-9250"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuval Wigderson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101521362","display_name":"Chuanqi Zhang","orcid":"https://orcid.org/0009-0004-4857-3454"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chuanqi Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11565572,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"1","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.1981000006198883,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.1981000006198883,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.1754000037908554,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.09380000084638596,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/computer-science","display_name":"Computer science","score":0.4638974666595459},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3579389452934265}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4638974666595459},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3579389452934265}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2025.v021a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2025.v021a001","pdf_url":"https://theoryofcomputing.org/articles/v021a001/v021a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2025.v021a001","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2025.v021a001","pdf_url":"https://theoryofcomputing.org/articles/v021a001/v021a001.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2911450482","display_name":null,"funder_award_id":"DGE-165651 8","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4385513050","display_name":null,"funder_award_id":"2024YFE0102500","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5267932457","display_name":"Graduate Research Fellowship Program (GRFP)","funder_award_id":"1656518","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7085497704","display_name":"AF: Medium: Theory of Computation - New Algorithmic and Hardness Techniques","funder_award_id":"1900460","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"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410927317.pdf","grobid_xml":"https://content.openalex.org/works/W4410927317.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"$":[0,1],"A":[2],"fundamental":[3],"fact":[4,125],"about":[5],"bounded-degree":[6],"graph":[7],"expanders":[8,91,223],"is":[9,34,86,121,142,173,180,190,199],"that":[10,75,83,126,221],"three":[11],"notions":[12,38,45],"of":[13,39,46,58,69,104,133,136,140,217],"expansion\u2014vertex":[14],"expansion,":[15,17,48,145,169],"edge":[16,134,144,168,184,197,204],"and":[18,60,72,106,114,151,178],"spectral":[19,67],"expansion\u2014are":[20],"all":[21],"equivalent.":[22],"In":[23],"this":[24,119],"paper,":[25],"we":[26,171],"study":[27],"to":[28,55,66,155,158,175,211],"what":[29],"extent":[30],"such":[31],"a":[32,163,193,212],"statement":[33],"true":[35],"for":[36],"linear-algebraic":[37,47,131],"expansion.":[40,160,185,205],"There":[41,88],"are":[42,89,93,128,224],"two":[43,129],"well-studied":[44],"namely,":[49],"dimension":[50,90,112,167,176,196,225],"expansion":[51,57,62,68,113,135,177,198],"(defined":[52,63],"in":[53,64,100],"analogy":[54,65],"vertex":[56],"graphs)":[59],"quantum":[61,95,143,159,183,203,222],"graphs).":[70],"Lubotzky":[71],"Zelmanov":[73],"proved":[74,154],"the":[76,79,84,101,109,124,187,218],"latter":[77],"implies":[78],"former.":[80],"We":[81,161],"prove":[82,172],"converse":[85],"false:":[87],"which":[92,146,152,170,179],"not":[94],"expanders.":[96,226],"This":[97,206],"also":[98,209],"answers":[99],"negative":[102],"questions":[103],"Lubotzky--Zelmanov":[105,219],"Dvir--Shpilka":[107],"on":[108],"relation":[110],"between":[111],"Kazhdan's":[115],"property":[116],"T.":[117],"Moreover,":[118],"asymmetry":[120],"explained":[122],"by":[123,149,182,192],"there":[127],"distinct":[130],"analogues":[132],"graphs.":[137],"The":[138],"first":[139],"these":[141],"was":[147],"introduced":[148],"Hastings,":[150],"he":[153],"be":[156],"equivalent":[157,174],"introduce":[162],"new":[164,207],"notion,":[165],"termed":[166],"implied":[181,191],"Thus,":[186],"separation":[188],"above":[189],"finer":[194],"one:":[195],"strictly":[200],"weaker":[201],"than":[202],"notion":[208],"leads":[210],"new,":[213],"more":[214],"modular":[215],"proof":[216],"result":[220]},"counts_by_year":[],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-06-01T00:00:00"}
