{"id":"https://openalex.org/W7225586090","doi":"https://doi.org/10.5281/zenodo.24064343","title":"The Kesten\u2013Stigum bound is sharp for the three-state Potts model on regular trees","display_name":"The Kesten\u2013Stigum bound is sharp for the three-state Potts model on regular trees","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225586090","doi":"https://doi.org/10.5281/zenodo.24064343"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24064343","doi":"https://doi.org/10.5281/zenodo.24064343","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24064343","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24064343","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041315596","display_name":"Yitzchak Shmalo","orcid":"https://orcid.org/0000-0002-2886-3049","observed_orcids":["https://orcid.org/0000-0002-2886-3049"]},"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":true,"raw_author_name":"Shmalo, Yitzchak","raw_affiliation_strings":["Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041315596"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9678000211715698,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9678000211715698,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.008799999952316284,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.008299999870359898,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/three-state-potts-model","display_name":"three-state Potts model","score":0.9300000071525574},{"id":"https://openalex.org/keywords/reconstruction-threshold","display_name":"reconstruction threshold","score":0.7570000290870667},{"id":"https://openalex.org/keywords/d-ary-trees","display_name":"d-ary trees","score":0.6830000281333923},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"belief propagation","score":0.6010000109672546},{"id":"https://openalex.org/keywords/normal-approximation","display_name":"Gaussian approximation","score":0.7720000147819519},{"id":"https://openalex.org/keywords/sharp-threshold","display_name":"sharp threshold","score":0.6330000162124634},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"computer-assisted proof","score":0.6010000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8646000027656555},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6503999829292297},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5658000111579895},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5264999866485596},{"id":"https://openalex.org/C98925819","wikidata":"https://www.wikidata.org/wiki/Q7235385","display_name":"Potts model","level":3,"score":0.5078999996185303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49729999899864197},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4277999997138977},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.40959998965263367},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.36959999799728394},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.26019999384880066}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24064343","doi":"https://doi.org/10.5281/zenodo.24064343","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24064343","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24064344","doi":"https://doi.org/10.5281/zenodo.24064344","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24064344","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24064343","doi":"https://doi.org/10.5281/zenodo.24064343","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24064343","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2042790585","https://openalex.org/W7225019892","https://openalex.org/W7224996434","https://openalex.org/W7225006468","https://openalex.org/W140324936","https://openalex.org/W2773669062","https://openalex.org/W1996199671","https://openalex.org/W2123607246","https://openalex.org/W7096225755","https://openalex.org/W2905373385"],"abstract_inverted_index":{"A":[0],"uniformly":[1],"random":[2],"colour":[3,21],"from":[4,8],"$\\{1,2,3\\}$":[5],"is":[6,82],"broadcast":[7],"the":[9,12,31,46,56,60,69,73,79,130,134,138],"root":[10,139],"of":[11,30,62,72,129,137],"infinite":[13],"$d$-ary":[14,80],"tree;":[15],"each":[16],"edge":[17],"keeps":[18],"its":[19],"parent's":[20],"with":[22,59],"probability":[23],"$\\lambda+(1-\\lambda)/3$":[24],"and":[25,42,64,88,91,118,145],"otherwise":[26],"moves":[27],"to":[28],"one":[29],"two":[32],"other":[33],"colours":[34,47],"uniformly.":[35],"We":[36],"prove":[37],"that":[38,68,101,109,156],"for":[39,84,95],"every":[40,43,85,150],"$d\\ge2$":[41],"$0\\le\\lambda\\le":[44],"d^{-1/2}$":[45],"at":[48,141],"depth":[49],"$n$":[50],"carry":[51],"asymptotically":[52],"no":[53],"information":[54],"about":[55],"root.":[57],"Together":[58],"theorem":[61],"Kesten":[63],"Stigum":[65],"this":[66,94],"shows":[67],"reconstruction":[70],"threshold":[71],"ferromagnetic":[74],"three-state":[75],"Potts":[76],"channel":[77],"on":[78],"tree":[81],"$\\lambda=d^{-1/2}$":[83],"degree.":[86],"Sly,":[87],"Mossel,":[89],"Sly":[90],"Sohn,":[92],"proved":[93],"all":[96],"degrees":[97],"above":[98],"a":[99,114,142],"constant":[100,110],"was":[102],"not":[103],"made":[104],"explicit.":[105],"Our":[106],"proof":[107],"makes":[108],"explicit,":[111],"$d\\ge91$,":[112],"by":[113,122],"quantitative":[115],"Gaussian":[116],"approximation,":[117],"covers":[119],"$2\\le":[120],"d\\le90$":[121],"computer-assisted":[123],"arguments:":[124],"an":[125],"exact":[126,146],"finite-state":[127],"upgrade":[128],"belief-propagation":[131,152],"recursion":[132],"bounds":[133],"second":[135],"moment":[136],"posterior":[140],"finite":[143],"depth,":[144],"polynomial":[147],"certificates":[148],"exclude":[149],"nontrivial":[151],"fixed":[153],"point":[154],"below":[155],"bound.":[157]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}