{"id":"https://openalex.org/W2399370712","doi":"https://doi.org/10.1137/130919143","title":"A Robust Khintchine Inequality, and Algorithms for Computing Optimal Constants in Fourier Analysis and High-Dimensional Geometry","display_name":"A Robust Khintchine Inequality, and Algorithms for Computing Optimal Constants in Fourier Analysis and High-Dimensional Geometry","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2399370712","doi":"https://doi.org/10.1137/130919143","mag":"2399370712"},"language":"en","primary_location":{"id":"doi:10.1137/130919143","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130919143","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5081127804","display_name":"Anindya De","orcid":"https://orcid.org/0000-0001-6795-8211"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anindya De","raw_affiliation_strings":["University of California at Berkeley"],"affiliations":[{"raw_affiliation_string":"University of California at Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054966819","display_name":"Ilias Diakonikolas","orcid":"https://orcid.org/0000-0002-5486-1856"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ilias Diakonikolas","raw_affiliation_strings":["Laboratory for Foundations of Computer Science"],"affiliations":[{"raw_affiliation_string":"Laboratory for Foundations of Computer Science","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014866889","display_name":"Rocco A. Servedio","orcid":"https://orcid.org/0000-0003-2407-543X"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rocco A. Servedio","raw_affiliation_strings":["Columbia University"],"affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081127804"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":5.4018,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.95773943,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"2","first_page":"1058","last_page":"1094"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.7787083387374878},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6962211728096008},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6480229496955872},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5725595951080322},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5524080991744995},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4836765229701996},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47112107276916504},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3663601279258728},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3335360884666443},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32267290353775024},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3010828495025635},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14551663398742676}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7787083387374878},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6962211728096008},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6480229496955872},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5725595951080322},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5524080991744995},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4836765229701996},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47112107276916504},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3663601279258728},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3335360884666443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32267290353775024},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3010828495025635},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14551663398742676},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130919143","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130919143","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1502986712","https://openalex.org/W1546372806","https://openalex.org/W1973271905","https://openalex.org/W1976165847","https://openalex.org/W1979694908","https://openalex.org/W1992053968","https://openalex.org/W2003672952","https://openalex.org/W2010549883","https://openalex.org/W2021646111","https://openalex.org/W2037982184","https://openalex.org/W2052617901","https://openalex.org/W2060775054","https://openalex.org/W2063836706","https://openalex.org/W2071439977","https://openalex.org/W2075045989","https://openalex.org/W2084217406","https://openalex.org/W2125208595","https://openalex.org/W2148858749","https://openalex.org/W2179261203","https://openalex.org/W2574800215","https://openalex.org/W2914539165","https://openalex.org/W2949874440","https://openalex.org/W3098578471","https://openalex.org/W4236046905"],"related_works":["https://openalex.org/W1529715114","https://openalex.org/W1978042415","https://openalex.org/W3038654277","https://openalex.org/W1996842245","https://openalex.org/W1516407058","https://openalex.org/W2740334431","https://openalex.org/W4212808623","https://openalex.org/W1994752097","https://openalex.org/W4281616812","https://openalex.org/W2966560432"],"abstract_inverted_index":{"This":[0,208],"paper":[1],"makes":[2],"two":[3],"contributions":[4],"towards":[5],"determining":[6],"some":[7,126],"well-studied":[8],"optimal":[9],"constants":[10],"in":[11,133,145,215,269],"Fourier":[12,45,61,165,330],"analysis":[13,334],"of":[14,47,101,140,153,173,222,232,254,267,278,324,326,335],"Boolean":[15],"functions":[16],"and":[17,28,54,77,84,170,218,240,296,303,308,332],"high-dimensional":[18],"geometry.":[19],"It":[20],"has":[21,42],"been":[22,292],"known":[23],"since":[24],"1994":[25],"[C.":[26],"Gotsman":[27],"N.":[29],"Linial,":[30],"Combinatorica,":[31],"14":[32],"(1994),":[33],"pp.":[34,94,301,315],"35--50]":[35],"that":[36,97,116,179,191,213,271],"every":[37,181],"linear":[38],"threshold":[39],"function":[40],"(LTF)":[41],"a":[43,137,187,241,274],"squared":[44,164],"mass":[46,62,166],"at":[48],"least":[49],"$1/2$":[50],"on":[51,111,167,289],"its":[52],"degree-$0$":[53,169],"degree-$1$":[55,171],"coefficients.":[56],"Let":[57,156],"the":[58,69,98,141,162,168,220,259],"minimum":[59,70,163,260],"such":[60,190],"be":[63,152,285],"${\\bf":[64,102,117,157,192,223],"W}^{\\leq":[65,103,118,158,193,198,203,224],"1}[{\\bf":[66,104,119,159,194,199,204,225],"LTF}]$,":[67],"where":[68],"is":[71,106,136,186,258,282],"taken":[72],"over":[73],"all":[74,78,262],"$n$-variable":[75,175],"LTFs":[76],"$n":[79],"\\ge":[80],"0$.":[81],"Benjamini,":[82],"Kalai,":[83],"Schramm":[85],"[Publ.":[86],"Math.":[87],"Inst.":[88],"Hautes":[89],"\u00c9tudes":[90],"Sci.,":[91],"90":[92],"(1999),":[93],"5--43]":[95],"conjectured":[96,283],"true":[99],"value":[100,188,221],"LTF}]$":[105,226],"$2/\\pi$.":[107],"We":[108,177,234],"make":[109],"progress":[110],"this":[112,257],"conjecture":[113],"by":[114,294,305],"proving":[115],"LTF}]":[120,195,205],"\\geq":[121],"1/2":[122],"+":[123,206],"c$":[124],"for":[125,180],"absolute":[127],"constant":[128,248,281],"$c>0$.":[129],"The":[130],"key":[131],"ingredient":[132],"our":[134],"proof":[135],"\u201crobust\u201d":[138],"version":[139],"well-known":[142],"Khintchine":[143],"inequality":[144],"functional":[146],"analysis,":[147,331],"which":[148],"we":[149],"believe":[150],"may":[151],"independent":[154,327],"interest.":[155],"LTF}_n]$":[160],"denote":[161],"coefficients":[172],"any":[174],"LTF.":[176],"prove":[178],"$\\eta":[182],">":[183],"0$,":[184],"there":[185],"$K=K(\\eta)=\\mathrm{poly}(1/\\eta)$":[189],"\\leq":[196,201],"{\\bf":[197,202],"LTF}_K]":[200],"\\eta.$":[207],"easily":[209],"yields":[210],"an":[211,229,236,251],"algorithm":[212],"runs":[214],"time":[216],"$2^{\\mathrm{poly}(1/\\eta)}$":[217],"determines":[219],"up":[227],"to":[228,245,249,284],"additive":[230,252],"error":[231,253],"$\\pm\\eta$.":[233],"give":[235],"analogous":[237],"structural":[238,318],"result,":[239],"similar":[242],"$2^{{\\mathrm{poly}(1/\\eta)}}$-time":[243],"algorithm,":[244],"determine":[246],"Tomaszewski's":[247,280],"within":[250,273],"$\\pm":[255],"\\eta$;":[256],"(over":[261],"origin-centered":[263],"hyperplanes":[264],"$H$)":[265],"fraction":[266],"points":[268],"$\\{-1,1\\}^n$":[270],"lie":[272],"Euclidean":[275],"distance":[276],"$1$":[277],"$H$.":[279],"$1/2$;":[286],"lower":[287],"bounds":[288],"it":[290],"have":[291],"given":[293],"Holzman":[295],"Kleitman":[297],"[Combinatorica,":[298],"12":[299],"(1992),":[300],"303--316]":[302],"independently":[304],"Ben-Tal,":[306],"Nemirovski,":[307],"Roos":[309],"[SIAM":[310],"J.":[311],"Optim.,":[312],"13":[313],"(2002),":[314],"535--560].":[316],"Our":[317],"results":[319],"combine":[320],"tools":[321],"from":[322],"anticoncentration":[323],"sums":[325],"random":[328],"variables,":[329],"Hermite":[333],"LTFs.":[336]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
