{"id":"https://openalex.org/W1905335549","doi":"https://doi.org/10.1145/3186590","title":"Invariance Principle on the Slice","display_name":"Invariance Principle on the Slice","publication_year":2018,"publication_date":"2018-04-13","ids":{"openalex":"https://openalex.org/W1905335549","doi":"https://doi.org/10.1145/3186590","mag":"1905335549"},"language":"en","primary_location":{"id":"doi:10.1145/3186590","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3186590","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1504.01689","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yuval Filmus","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Yuval Filmus","raw_affiliation_strings":["Technion \u2014 Israel Institute of Technology, Haifa, Israel","Technion \u00ad Israel Institute of Technology, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technion \u2014 Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Technion \u00ad Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083621825","display_name":"Guy Kindler","orcid":"https://orcid.org/0000-0002-3384-3720"},"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"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Guy Kindler","raw_affiliation_strings":["The Hebrew University, Jerusalem, Israel","The Hebrew University; Jerusalem Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"The Hebrew University; Jerusalem Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013467728","display_name":"Elchanan Mossel","orcid":"https://orcid.org/0000-0001-7812-7886"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elchanan Mossel","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, Massachusetts","Massachusetts Institute of Technology, Cambridge, Massachusetts#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, Massachusetts","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, Massachusetts#TAB#","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042196132","display_name":"Karl Wimmer","orcid":null},"institutions":[{"id":"https://openalex.org/I165102784","display_name":"Duquesne University","ror":"https://ror.org/02336z538","country_code":"US","type":"education","lineage":["https://openalex.org/I165102784"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Karl Wimmer","raw_affiliation_strings":["Duquesne University, Pittsburgh, Pennsylvania","Duquesne University. Pittsburgh, Pennsylvania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Duquesne University, Pittsburgh, Pennsylvania","institution_ids":["https://openalex.org/I165102784"]},{"raw_affiliation_string":"Duquesne University. Pittsburgh, Pennsylvania","institution_ids":["https://openalex.org/I165102784"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00769769,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"10","issue":"3","first_page":"1","last_page":"37"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9986000061035156,"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":0.6386271119117737},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6320621967315674},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.49611935019493103},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.4841633439064026},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47296303510665894},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45785295963287354},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45226022601127625},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.4364311099052429},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4167414903640747},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.4068419635295868},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3675041198730469},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1934821605682373},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15611621737480164},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14501547813415527},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13312473893165588}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6386271119117737},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6320621967315674},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.49611935019493103},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.4841633439064026},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47296303510665894},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45785295963287354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45226022601127625},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.4364311099052429},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4167414903640747},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4068419635295868},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3675041198730469},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1934821605682373},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15611621737480164},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14501547813415527},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13312473893165588},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1145/3186590","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3186590","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1504.01689","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.01689","pdf_url":"https://arxiv.org/pdf/1504.01689","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":"pmh:oai:drops-oai.dagstuhl.de:5823","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.15","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol050-ccc2016/LIPIcs.CCC.2016.15/LIPIcs.CCC.2016.15.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"","raw_type":"InProceedings"},{"id":"mag:1905335549","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1504.01689","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:CiteSeerX.psu:10.1.1.713.1610","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.713.1610","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/%7Eyuvalf/invariance.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/135811","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/135811","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"other univ website","raw_type":"http://purl.org/eprint/type/ConferencePaper"},{"id":"doi:10.48550/arxiv.1504.01689","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1504.01689","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":"Preprint"},{"id":"doi:10.4230/lipics.ccc.2016.15","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.ccc.2016.15","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"mag:2871506789","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/conf/coco/coco2016.html#FilmusKMW16","pdf_url":null,"source":{"id":"https://openalex.org/S4306418030","display_name":"Conference on Computational Complexity","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Conference on Computational Complexity","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1504.01689","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.01689","pdf_url":"https://arxiv.org/pdf/1504.01689","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1203863711","display_name":"AF: Small: Boolean Functions: Inequalities, Structure, Algorithms & Hardness","funder_award_id":"1320105","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G179868298","display_name":null,"funder_award_id":"N00014-14-1-0823","funder_id":"https://openalex.org/F4320306078","funder_display_name":"U.S. Department of Defense"},{"id":"https://openalex.org/G241557827","display_name":null,"funder_award_id":"N00014-14-1-0823","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G2417798575","display_name":null,"funder_award_id":"DMS 1106999","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G2938749385","display_name":"Combinatorial Statistics and Quantitative Social Choice","funder_award_id":"1106999","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4062780233","display_name":"Research in Mathematics","funder_award_id":"1128155","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4094641253","display_name":null,"funder_award_id":"328025","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G414571026","display_name":null,"funder_award_id":"DMS-1128155","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G4170996789","display_name":null,"funder_award_id":"DMS 1106999","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4746377364","display_name":null,"funder_award_id":"328025","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5453703545","display_name":"AF:Small:RUI:New directions in Fourier analysis, noise sensitivity, and learning theory","funder_award_id":"1117079","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G647586973","display_name":null,"funder_award_id":"DMS-1128155","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7807443570","display_name":null,"funder_award_id":"DMS 1106999, CCF 1320105 and CCF 1117079","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8937994240","display_name":null,"funder_award_id":"328025","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W4985749","https://openalex.org/W1486325209","https://openalex.org/W1550204818","https://openalex.org/W1891181203","https://openalex.org/W1969865855","https://openalex.org/W1978122435","https://openalex.org/W1987233725","https://openalex.org/W1987406389","https://openalex.org/W1989761515","https://openalex.org/W1992472342","https://openalex.org/W2006901918","https://openalex.org/W2019935404","https://openalex.org/W2042179958","https://openalex.org/W2047141034","https://openalex.org/W2049098250","https://openalex.org/W2053464741","https://openalex.org/W2056842939","https://openalex.org/W2068998342","https://openalex.org/W2071505449","https://openalex.org/W2078289947","https://openalex.org/W2078929687","https://openalex.org/W2087326429","https://openalex.org/W2124580341","https://openalex.org/W2143698439","https://openalex.org/W2153305111","https://openalex.org/W2171695231","https://openalex.org/W2331602765","https://openalex.org/W2570644248","https://openalex.org/W2963876362","https://openalex.org/W4238088164","https://openalex.org/W4243396289"],"related_works":["https://openalex.org/W3102361875","https://openalex.org/W2118409018","https://openalex.org/W1585934788","https://openalex.org/W3197625049","https://openalex.org/W768490941","https://openalex.org/W2547088347","https://openalex.org/W2795414768","https://openalex.org/W2963847608","https://openalex.org/W2060782772","https://openalex.org/W1799827283","https://openalex.org/W20105556","https://openalex.org/W2035231739","https://openalex.org/W1558669467","https://openalex.org/W2963846517","https://openalex.org/W2963186189","https://openalex.org/W2230984504","https://openalex.org/W2147989485","https://openalex.org/W2773806639","https://openalex.org/W2130233653","https://openalex.org/W1891303997"],"abstract_inverted_index":{"The":[0,79,179,248],"non-linear":[1],"invariance":[2,80,114,281],"principle":[3,81,115,282],"of":[4,32,50,121,187,232,271,315,324,342,353,359,368,376,386,401,404],"Mossel,":[5],"O\u2019Donnell,":[6],"and":[7,70,148,154,157,265,304,364,378,390,393],"Oleszkiewicz":[8],"establishes":[9],"that":[10,98,141],"if":[11,33],"f":[12,34,51],"(":[13,35,52,125,224,235,285,299,305],"x":[14,18,236,239],"1":[15,37,54,127,134,164,174,201,237,287,307],",\u2026":[16,128,135,165,202,308],",":[17,129,136,166,203,309,329],"n":[19,40,57,131,138,168,177,205,226,240,242,290,301,311,316,325],")":[20,41,139,229,291,312,320],"is":[21,42,93,104,182,217,279,292,344],"a":[22,297,340,351,357,365,384],"multilinear":[23],"low-degree":[24],"polynomial":[25],"with":[26,243],"low":[27],"influences,":[28],"then":[29],"the":[30,48,91,99,107,161,185,188,208,218,222,269,272,293,349,360,369,405,415],"distribution":[31,49,220,295],"b":[36,39],",\u2026,":[38,55,175,238,288],"close":[43],"(in":[44,268],"various":[45],"senses)":[46],"to":[47,184,197],"G":[53,56,71],"),":[58],"where":[59],"B":[60],"i":[61,72,147,150],"\u2208":[62],"R":[63],"{-1,1}":[64],"are":[65,75,169,172,211],"independent":[66,76,317,326],"Bernoulli":[67],"random":[68,123,321,334],"variables":[69,124,162],"\u223c":[73],"N(0,1)":[74],"standard":[77],"Gaussians.":[78],"has":[82],"seen":[83],"many":[84],"applications":[85],"in":[86,191,206,252,283],"theoretical":[87,253],"computer":[88,254],"science,":[89],"including":[90],"Majority":[92,343],"Stablest":[94,345],"conjecture,":[95],"which":[96,207,230,284,408],"shows":[97,250],"Goemans\u2013Williamson":[100],"algorithm":[101],"for":[102,117,346,414],"MAX-CUT":[103],"optimal":[105],"under":[106],"Unique":[108],"Games":[109],"Conjecture.":[110],"More":[111],"generally,":[112],"MOO\u2019s":[113],"works":[116],"any":[118],"two":[119],"vectors":[120,234],"hypercontractive":[122],"X":[126,130,146,163,167,200,204,286,289],"),(":[132],"Y":[133,137,149,173,176,306,310],"such":[140],"(i)":[142],"Matching":[143],"moments":[144,156],":":[145,160],"have":[151],"matching":[152],"first":[153,406],"second":[155],"(ii)":[158],"Independence":[159],"independent,":[170],"as":[171],".":[178,247],"independence":[180],"condition":[181],"crucial":[183],"proof":[186,381],"theorem,":[189,356,363,373],"yet":[190],"some":[192],"cases":[193],"we":[194,338,397],"would":[195],"like":[196],"use":[198,400],"distributions":[199],"individual":[209],"coordinates":[210],"not":[212],"independent.":[213],"A":[214],"common":[215],"example":[216],"uniform":[219,294],"on":[221,296,348,383],"slice":[223,249,298],"[":[225,300],"]":[227,302],"k":[228,246],"consists":[231,313],"all":[233],")\u2208{0,1}":[241],"Hamming":[244],"weight":[245],"up":[251],"science":[255],"(hardness":[256],"amplification,":[257],"direct":[258],"sum":[259],"testing),":[260],"extremal":[261],"combinatorics":[262],"(Erd\u0151s\u2013Ko\u2013Rado":[263],"theorems),":[264],"coding":[266],"theory":[267],"guise":[270],"Johnson":[273],"association":[274],"scheme).":[275],"Our":[276,380],"main":[277],"result":[278],"an":[280,410],"pn":[303],"either":[314],"Ber(":[318],"p":[319,328,330,332],"variables,":[322],"or":[323],"N(":[327],"(1-":[331],"))":[333],"variables.":[335],"As":[336],"applications,":[337],"prove":[339],"version":[341,352,358,367],"functions":[347],"slice,":[350],"Bourgain\u2019s":[354],"tail":[355],"Kindler\u2013Safra":[361],"structural":[362],"stability":[366],"t":[370],"-intersecting":[371],"Erd\u0151s\u2013Ko\u2013Rado":[372],"combining":[374],"techniques":[375],"Wilson":[377],"Friedgut.":[379],"relies":[382],"combination":[385],"ideas":[387],"from":[388],"analysis":[389],"probability,":[391],"algebra,":[392],"combinatorics.":[394],"In":[395],"particular,":[396],"make":[398],"essential":[399],"recent":[402],"work":[403],"author":[407],"describes":[409],"explicit":[411],"Fourier":[412],"basis":[413],"slice.":[416]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
