{"id":"https://openalex.org/W2964239702","doi":"https://doi.org/10.1145/3055399.3055420","title":"Information-theoretic thresholds from the cavity method","display_name":"Information-theoretic thresholds from the cavity method","publication_year":2017,"publication_date":"2017-06-15","ids":{"openalex":"https://openalex.org/W2964239702","doi":"https://doi.org/10.1145/3055399.3055420","mag":"2964239702"},"language":"en","primary_location":{"id":"doi:10.1145/3055399.3055420","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3055399.3055420","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-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/A5044991483","display_name":"Amin Coja\u2010Oghlan","orcid":"https://orcid.org/0000-0002-7350-1418"},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Amin Coja-Oghlan","raw_affiliation_strings":["Goethe University Frankfurt, Germany"],"affiliations":[{"raw_affiliation_string":"Goethe University Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068236230","display_name":"Florent Krz\u0105ka\u0142a","orcid":"https://orcid.org/0000-0003-2313-2578"},"institutions":[{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"funder","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Florent Krzakala","raw_affiliation_strings":["CNRS, France / PSL Research University, France / ENS, France / UPMC, France"],"affiliations":[{"raw_affiliation_string":"CNRS, France / PSL Research University, France / ENS, France / UPMC, France","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010848870","display_name":"Will Perkins","orcid":"https://orcid.org/0000-0002-7937-7016"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Will Perkins","raw_affiliation_strings":["University of Birmingham, UK"],"affiliations":[{"raw_affiliation_string":"University of Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089268172","display_name":"Lenka Zdeborov\u00e1","orcid":"https://orcid.org/0000-0002-8377-3978"},"institutions":[{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"funder","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210128565","display_name":"CEA Paris-Saclay","ror":"https://ror.org/03n15ch10","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210128565"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lenka Zdeborova","raw_affiliation_strings":["CNRS, France / CEA, France / University of Paris-Saclay, France"],"affiliations":[{"raw_affiliation_string":"CNRS, France / CEA, France / University of Paris-Saclay, France","institution_ids":["https://openalex.org/I277688954","https://openalex.org/I1294671590","https://openalex.org/I4210128565","https://openalex.org/I2738703131"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044991483"],"corresponding_institution_ids":["https://openalex.org/I114090438"],"apc_list":null,"apc_paid":null,"fwci":3.3223,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.94013938,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"146","last_page":"157"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/conjecture","display_name":"Conjecture","score":0.6785634756088257},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6594762802124023},{"id":"https://openalex.org/keywords/replica","display_name":"Replica","score":0.5697628855705261},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.5498894453048706},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.5455363392829895},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5430062413215637},{"id":"https://openalex.org/keywords/stochastic-block-model","display_name":"Stochastic block model","score":0.48809897899627686},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4798992872238159},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4679509401321411},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4395356774330139},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43160080909729004},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.4230071008205414},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4077981114387512},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.27911102771759033},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1407923698425293},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11797741055488586},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09872597455978394}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6785634756088257},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6594762802124023},{"id":"https://openalex.org/C2775937380","wikidata":"https://www.wikidata.org/wiki/Q1232589","display_name":"Replica","level":2,"score":0.5697628855705261},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.5498894453048706},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.5455363392829895},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5430062413215637},{"id":"https://openalex.org/C2779982251","wikidata":"https://www.wikidata.org/wiki/Q25053762","display_name":"Stochastic block model","level":3,"score":0.48809897899627686},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4798992872238159},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4679509401321411},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4395356774330139},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43160080909729004},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.4230071008205414},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4077981114387512},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.27911102771759033},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1407923698425293},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11797741055488586},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09872597455978394},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3055399.3055420","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3055399.3055420","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3166933268","display_name":null,"funder_award_id":"278857-PTCC, 307087-SPARCS","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G7926746001","display_name":"New approaches to Gibbs measures at the interface of probability and computational complexity","funder_award_id":"EP/P009913/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8342849666","display_name":null,"funder_award_id":"EP/P009913/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":78,"referenced_works":["https://openalex.org/W179407972","https://openalex.org/W385466589","https://openalex.org/W904137795","https://openalex.org/W1489398757","https://openalex.org/W1510846731","https://openalex.org/W1518885151","https://openalex.org/W1534224368","https://openalex.org/W1572652170","https://openalex.org/W1598946980","https://openalex.org/W1677159791","https://openalex.org/W1818081266","https://openalex.org/W1867676345","https://openalex.org/W1914749871","https://openalex.org/W1971493102","https://openalex.org/W1972913305","https://openalex.org/W1974967023","https://openalex.org/W1978113428","https://openalex.org/W1991809010","https://openalex.org/W2004531067","https://openalex.org/W2012724629","https://openalex.org/W2018836315","https://openalex.org/W2019705392","https://openalex.org/W2023348178","https://openalex.org/W2037787045","https://openalex.org/W2042038477","https://openalex.org/W2042464140","https://openalex.org/W2064282083","https://openalex.org/W2070702809","https://openalex.org/W2078168527","https://openalex.org/W2082249316","https://openalex.org/W2088419249","https://openalex.org/W2105546154","https://openalex.org/W2105860081","https://openalex.org/W2114351639","https://openalex.org/W2115831572","https://openalex.org/W2116061856","https://openalex.org/W2131991992","https://openalex.org/W2139585907","https://openalex.org/W2146712141","https://openalex.org/W2147880316","https://openalex.org/W2151781750","https://openalex.org/W2152182443","https://openalex.org/W2156595614","https://openalex.org/W2160844215","https://openalex.org/W2161410247","https://openalex.org/W2168290833","https://openalex.org/W2171001107","https://openalex.org/W2179644698","https://openalex.org/W2196782699","https://openalex.org/W2233026804","https://openalex.org/W2254463431","https://openalex.org/W2266756552","https://openalex.org/W2271176746","https://openalex.org/W2287686747","https://openalex.org/W2326292785","https://openalex.org/W2332339252","https://openalex.org/W2548129158","https://openalex.org/W2565889208","https://openalex.org/W2566505556","https://openalex.org/W2802739963","https://openalex.org/W2913668833","https://openalex.org/W2952834582","https://openalex.org/W2962896009","https://openalex.org/W2963383801","https://openalex.org/W2963892318","https://openalex.org/W2963994072","https://openalex.org/W3099994871","https://openalex.org/W3101041417","https://openalex.org/W3105177482","https://openalex.org/W3105442588","https://openalex.org/W3105609882","https://openalex.org/W3106164415","https://openalex.org/W3106214974","https://openalex.org/W3142570770","https://openalex.org/W4213277474","https://openalex.org/W4233762729","https://openalex.org/W4241963438","https://openalex.org/W4292232932"],"related_works":["https://openalex.org/W2796901439","https://openalex.org/W2977688136","https://openalex.org/W4301017148","https://openalex.org/W4283448257","https://openalex.org/W4316829854","https://openalex.org/W2754525922","https://openalex.org/W1937904582","https://openalex.org/W3088247692","https://openalex.org/W3048055536","https://openalex.org/W3102036813"],"abstract_inverted_index":{"Vindicating":[0],"a":[1,13,72,81,110],"sophisticated":[2],"but":[3],"non-rigorous":[4],"physics":[5],"approach":[6,127],"called":[7],"the":[8,16,31,34,38,55,86,89,114,119,126],"cavity":[9,120],"method,":[10,121],"we":[11,84,123],"establish":[12,85],"formula":[14,87],"for":[15,88],"mutual":[17,90],"information":[18,91],"in":[19,37,60,92,99],"statistical":[20],"inference":[21],"problems":[22,64],"induced":[23],"by":[24],"random":[25,61,67],"graphs.":[26],"This":[27],"general":[28],"result":[29],"implies":[30],"conjecture":[32,73],"on":[33,103],"information-theoretic":[35],"threshold":[36],"disassortative":[39],"stochastic":[40],"block":[41],"model":[42],"[Decelle":[43],"et":[44,76],"al.:":[45,77],"Phys.":[46],"Rev.":[47],"E":[48],"(2011)]":[49],"and":[50,122],"allows":[51],"us":[52],"to":[53],"pinpoint":[54],"exact":[56],"condensation":[57],"phase":[58],"transition":[59],"constraint":[62],"satisfaction":[63],"such":[65],"as":[66,97],"graph":[68],"coloring,":[69],"thereby":[70],"proving":[71],"from":[74],"[Krzakala":[75],"PNAS":[78],"(2007)].":[79],"As":[80],"further":[82],"application":[83],"Low-Density":[93],"Generator":[94],"Matrix":[95],"codes":[96],"conjectured":[98],"[Montanari:":[100],"IEEE":[101],"Transactions":[102],"Information":[104],"Theory":[105],"(2005)].":[106],"The":[107],"proofs":[108],"provide":[109],"conceptual":[111],"underpinning":[112],"of":[113,118],"replica":[115],"symmetric":[116],"variant":[117],"expect":[124],"that":[125],"will":[128],"find":[129],"many":[130],"future":[131],"applications.":[132]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}