{"id":"https://openalex.org/W2418078036","doi":"https://doi.org/10.1017/s096354831600016x","title":"Mixing, Communication Complexity and Conjectures of Gowers and Viola","display_name":"Mixing, Communication Complexity and Conjectures of Gowers and Viola","publication_year":2016,"publication_date":"2016-06-07","ids":{"openalex":"https://openalex.org/W2418078036","doi":"https://doi.org/10.1017/s096354831600016x","mag":"2418078036"},"language":"en","primary_location":{"id":"doi:10.1017/s096354831600016x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831600016x","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029334678","display_name":"Aner Shalev","orcid":"https://orcid.org/0000-0001-9428-2958"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]},{"id":"https://openalex.org/I4210092592","display_name":"Einstein Institute of Science","ror":"https://ror.org/00ftze589","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210092592"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["BG","CZ","IL","IN"],"is_corresponding":true,"raw_author_name":"ANER SHALEV","raw_affiliation_strings":["Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail:","Einstein Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail:","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"Einstein Institute of Mathematics","institution_ids":["https://openalex.org/I4210092592","https://openalex.org/I4210105926","https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029334678"],"corresponding_institution_ids":["https://openalex.org/I197251160","https://openalex.org/I4210092592","https://openalex.org/I4210105926","https://openalex.org/I4210120266"],"apc_list":null,"apc_paid":null,"fwci":3.9742,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.93071865,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"26","issue":"4","first_page":"628","last_page":"640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9969000220298767,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9969000220298767,"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/T10849","display_name":"Finite Group Theory Research","score":0.98089998960495,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9739000201225281,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7725428938865662},{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.7674514651298523},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7268859148025513},{"id":"https://openalex.org/keywords/simple-group","display_name":"Simple group","score":0.6451126933097839},{"id":"https://openalex.org/keywords/classification-of-finite-simple-groups","display_name":"Classification of finite simple groups","score":0.6336697340011597},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5338343977928162},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.51654452085495},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4745510518550873},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.46414175629615784},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.411312460899353},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39065563678741455},{"id":"https://openalex.org/keywords/group-of-lie-type","display_name":"Group of Lie type","score":0.38533109426498413},{"id":"https://openalex.org/keywords/group-theory","display_name":"Group theory","score":0.3041408061981201},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2291458547115326},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08574911952018738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7725428938865662},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.7674514651298523},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7268859148025513},{"id":"https://openalex.org/C5383885","wikidata":"https://www.wikidata.org/wiki/Q571124","display_name":"Simple group","level":3,"score":0.6451126933097839},{"id":"https://openalex.org/C63388996","wikidata":"https://www.wikidata.org/wiki/Q1340623","display_name":"Classification of finite simple groups","level":4,"score":0.6336697340011597},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5338343977928162},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.51654452085495},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4745510518550873},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.46414175629615784},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.411312460899353},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39065563678741455},{"id":"https://openalex.org/C51997251","wikidata":"https://www.wikidata.org/wiki/Q1406425","display_name":"Group of Lie type","level":3,"score":0.38533109426498413},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.3041408061981201},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2291458547115326},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08574911952018738},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s096354831600016x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831600016x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W11109725","https://openalex.org/W120124575","https://openalex.org/W1498353858","https://openalex.org/W1598525823","https://openalex.org/W1995343556","https://openalex.org/W2001753575","https://openalex.org/W2001825657","https://openalex.org/W2004419620","https://openalex.org/W2007263799","https://openalex.org/W2010699490","https://openalex.org/W2059314328","https://openalex.org/W2060489837","https://openalex.org/W2064651061","https://openalex.org/W2069193826","https://openalex.org/W2071421100","https://openalex.org/W2125459682","https://openalex.org/W2912205456","https://openalex.org/W2963357159","https://openalex.org/W4230529945"],"related_works":["https://openalex.org/W1986567673","https://openalex.org/W2594545647","https://openalex.org/W2490903239","https://openalex.org/W2021883390","https://openalex.org/W4378909075","https://openalex.org/W4296471573","https://openalex.org/W2952246509","https://openalex.org/W1598549886","https://openalex.org/W2046195881","https://openalex.org/W2074054142"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,41,60,134,163,171],"distribution":[3],"of":[4,6,27,34,43,96,174,183,206,209],"products":[5,50,182],"conjugacy":[7],"classes":[8],"in":[9],"finite":[10,68,80,203,226],"simple":[11,69,81,204,227],"groups,":[12],"obtaining":[13],"effective":[14],"two-step":[15],"mixing":[16],"results,":[17,30],"which":[18],"give":[19],"rise":[20],"to":[21,24,40,65,162,180],"an":[22,175],"approximation":[23],"a":[25,79,102,105,111,137,141,148,184,202],"conjecture":[26],"Thompson.":[28],"Our":[29],"combined":[31],"with":[32,160],"work":[33,58],"Gowers":[35],"and":[36,51,83,116,212],"Viola,":[37],"also":[38,168],"lead":[39],"solution":[42],"recent":[44],"conjectures":[45],"they":[46],"posed":[47],"on":[48,59,155],"interleaved":[49,135,181],"related":[52,179],"complexity":[53,173],"lower":[54],"bounds,":[55],"extending":[56],"their":[57],"groups":[61],"SL(2,":[62],"q":[63],")":[64,113,128],"all":[66],"(non-abelian)":[67],"groups.":[70],"In":[71],"particular":[72],"it":[73],"follows":[74,169],"that,":[75],"if":[76],"G":[77,88,156,188,197,200,220,223],"is":[78,152,190,201,224],"group,":[82],"A":[84,115],",":[85,107,122,185],"B":[86,130],"\u2286":[87],"t":[89,91,112,127,149,151,189,194,216],"for":[90],"\u2a7e":[92],"2":[93],"are":[94,131,232],"subsets":[95],"fixed":[97],"positive":[98],"densities,":[99],"then,":[100],"as":[101],"=":[103,118],"(":[104,119],"1":[106,121,142,144],".":[108,109,123,124,145,146,147],".,":[110,125],"\u2208":[114,129,187],"b":[117,120,126,139,143,150,186],"chosen":[132],"uniformly,":[133],"product":[136],"\u2022":[138],":=":[140],"almost":[153],"uniform":[154],"(with":[157],"quantitative":[158],"estimates)":[159],"respect":[161],"\u2113":[164],"\u221e":[165],"-norm.":[166],"It":[167],"that":[170],"communication":[172],"old":[176],"decision":[177],"problem":[178],"at":[191,213],"least":[192,214],"\u03a9(":[193,215],"log":[195,217,218],"|":[196,219],"|)":[198,221],"when":[199,222],"group":[205],"Lie":[207],"type":[208],"bounded":[210],"rank,":[211],"any":[225],"group.":[228],"Both":[229],"these":[230],"bounds":[231],"best":[233],"possible.":[234]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
