{"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":5,"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":0.12154065,"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/G2499887605","display_name":null,"funder_award_id":"DGE-1656518","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G320138474","display_name":null,"funder_award_id":"-1656518","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":null,"funder_award_id":"1656518","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6008157674","display_name":null,"funder_award_id":"CCF-1900460","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7085497704","display_name":null,"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":{"A":[0],"fundamental":[1],"fact":[2,117],"about":[3],"bounded-degree":[4],"graph":[5],"expanders":[6,85],"is":[7,31,80,113,133,163,170,179],"that":[8,70,77,118],"three":[9],"notions":[10,35,41],"of":[11,36,42,54,65,97,125,128,131],"expansion-vertex":[12],"expansion,":[13,15,44,136,159],"edge":[14,126,135,158,174,186],"and":[16,56,67,99,107,142,168],"spectral":[17,63],"expansion-are":[18],"all":[19],"equivalent.In":[20],"this":[21,111],"paper,":[22],"we":[23,161],"study":[24],"to":[25,51,62,146,149,165],"what":[26],"extent":[27],"such":[28],"a":[29,153,182],"statement":[30],"true":[32],"for":[33],"linear-algebraic":[34,43],"expansion.There":[37],"are":[38,83,87,120],"two":[39,121],"well-studied":[40],"namely,":[45],"dimension":[46,84,105,157,166,185],"expansion":[47,53,58,64,106,127,167],"(defined":[48,59],"in":[49,60,93],"analogy":[50,61],"vertex":[52],"graphs)":[55],"quantum":[57,89,134,150,173],"graphs).Lubotzky":[66],"Zelmanov":[68],"proved":[69,145],"the":[71,74,78,94,102,116,176],"latter":[72],"implies":[73],"former.We":[75],"prove":[76,162],"converse":[79],"false:":[81],"There":[82],"which":[86,137,143,160,169],"not":[88],"expanders.This":[90],"also":[91],"answers":[92],"negative":[95],"questions":[96],"Lubotzky-Zelmanov":[98],"Dvir-Shpilka":[100],"on":[101],"relation":[103],"between":[104],"Kazhdan's":[108],"property":[109],"T.Moreover,":[110],"asymmetry":[112],"explained":[114],"by":[115,140,172,181],"there":[119],"distinct":[122],"linearalgebraic":[123],"analogues":[124],"graphs.The":[129],"first":[130],"these":[132],"was":[138],"introduced":[139],"Hastings,":[141],"he":[144],"be":[147],"equivalent":[148,164],"expansion.We":[151],"introduce":[152],"new":[154],"notion,":[155],"termed":[156],"implied":[171,180],"expansion.Thus,":[175],"separation":[177],"above":[178],"finer":[183],"one:":[184]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-06-01T00:00:00"}
