{"id":"https://openalex.org/W7204535598","doi":"https://doi.org/10.48550/arxiv.2608.26259","title":"Information Percolation and cutoff for Potts Glauber Dynamics","display_name":"Information Percolation and cutoff for Potts Glauber Dynamics","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7204535598","doi":"https://doi.org/10.48550/arxiv.2608.26259"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.26259","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26259","pdf_url":"https://arxiv.org/pdf/2608.26259","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.26259","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148554384","display_name":"Seoyeon Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yang, Seoyeon","raw_affiliation_strings":["Department of Mathematics , Princeton University , Princeton , NJ 08540 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Princeton University , Princeton , NJ 08540 , USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076570918","display_name":"Allan Sly","orcid":"https://orcid.org/0009-0004-8183-1910","observed_orcids":["https://orcid.org/0009-0004-8183-1910"]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sly, Allan","raw_affiliation_strings":["Department of Mathematics , Princeton University , Princeton , NJ 08540 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Princeton University , Princeton , NJ 08540 , USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9771000146865845,"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":0.9771000146865845,"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":0.01140000019222498,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.0034000000450760126,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/potts-model","display_name":"Potts model","score":0.7689999938011169},{"id":"https://openalex.org/keywords/glauber-dynamics","display_name":"Glauber dynamics","score":0.9959999918937683},{"id":"https://openalex.org/keywords/cut-off","display_name":"cut-off","score":0.6230000257492065},{"id":"https://openalex.org/keywords/mixing-time","display_name":"mixing time","score":0.984000027179718},{"id":"https://openalex.org/keywords/color-bias","display_name":"color bias","score":0.6420000195503235},{"id":"https://openalex.org/keywords/random-polymers","display_name":"random polymers","score":0.7870000004768372},{"id":"https://openalex.org/keywords/ferromagnetic-spin-systems","display_name":"ferromagnetic spin systems","score":0.8130000233650208},{"id":"https://openalex.org/keywords/discrete-torus","display_name":"discrete torus","score":0.8420000076293945},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.5680000185966492}],"concepts":[{"id":"https://openalex.org/C98925819","wikidata":"https://www.wikidata.org/wiki/Q7235385","display_name":"Potts model","level":3,"score":0.7379999756813049},{"id":"https://openalex.org/C2780708879","wikidata":"https://www.wikidata.org/wiki/Q5567254","display_name":"Glauber","level":3,"score":0.7293999791145325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6626999974250793},{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.6378999948501587},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.49970000982284546},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.48339998722076416},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3944999873638153},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.37689998745918274},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.37540000677108765},{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.3578000068664551},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.3546000123023987},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3230000138282776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29820001125335693},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C107277493","wikidata":"https://www.wikidata.org/wiki/Q5101824","display_name":"Chiral Potts curve","level":4,"score":0.28380000591278076},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C150775274","wikidata":"https://www.wikidata.org/wiki/Q1490646","display_name":"Spin glass","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2565000057220459}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.26259","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26259","pdf_url":"https://arxiv.org/pdf/2608.26259","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.26259","doi":"https://doi.org/10.48550/arxiv.2608.26259","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.26259","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.26259","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26259","pdf_url":"https://arxiv.org/pdf/2608.26259","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204535598.pdf","grobid_xml":"https://content.openalex.org/works/W7204535598.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7167629675"],"related_works":["https://openalex.org/W1977452791","https://openalex.org/W1906977363","https://openalex.org/W2965166794","https://openalex.org/W7168295401","https://openalex.org/W2962813956","https://openalex.org/W2990262217","https://openalex.org/W2969331024","https://openalex.org/W7131417026","https://openalex.org/W7222612792","https://openalex.org/W4415329339"],"abstract_inverted_index":{"We":[0,195,239],"prove":[1,129],"cutoff":[2,46,130],"with":[3],"an":[4,49,80,144,184],"$O(1)$":[5,51],"window":[6,52],"for":[7,32,43,131,162,167,227],"the":[8,14,20,45,62,68,73,87,91,96,101,111,117,122,148,155,163,172,180,202,218,222,229],"continuous-time":[9],"heat-bath":[10],"Glauber":[11],"dynamics":[12],"of":[13,67,103,125,151,154,251],"ferromagnetic":[15],"$q$-state":[16],"Potts":[17,173],"model":[18],"on":[19,147],"discrete":[21],"torus":[22],"$\u039b_n=(\\mathbb":[23],"Z/n\\mathbb":[24],"Z)^d$":[25],"at":[26,54,89],"sufficiently":[27],"high":[28],"temperature.":[29],"More":[30],"precisely,":[31],"every":[33],"fixed":[34],"$d\\ge2$":[35],"and":[36,209,237],"$q\\ge3$,":[37],"there":[38],"exists":[39],"$\u03b2_0=\u03b2_0(d,q)>0$":[40],"such":[41],"that,":[42],"$0<\u03b2<\u03b2_0$,":[44],"occurs":[47],"in":[48,246],"optimal":[50],"centered":[53],"\\[":[55],"t_\\star=t_\\star^{(n)}:=\\frac{1}{2\\mathfrak{r}}\\log":[56],"|\u039b_n|,":[57],"\\]":[58],"where":[59],"$\\mathfrak{r}\\in(0,1)$":[60],"is":[61,76,84,121,160,188],"exact":[63],"exponential":[64],"decay":[65],"rate":[66],"one-site":[69],"color":[70,118],"bias.":[71,119],"Thus,":[72],"mixing":[74,149],"time":[75,88,150,158],"determined":[77],"up":[78],"to":[79,128,212,216],"additive":[81],"\\(O(1)\\).":[82],"It":[83],"characterized":[85],"by":[86,190],"which":[90,159],"macroscopic":[92],"color-density":[93],"bias":[94,220],"from":[95,221],"monochromatic":[97,112],"initial":[98,113,223],"condition":[99,114],"enters":[100],"scale":[102],"equilibrium":[104],"fluctuations.":[105],"Moreover,":[106],"our":[107],"proof":[108],"shows":[109],"that":[110,187,200],"uniquely":[115],"maximizes":[116],"This":[120,225],"first":[123],"implementation":[124],"information":[126,140,203],"percolation":[127,141,204],"a":[132,137,191,197,233,247],"non-monotone":[133,169],"spin":[134],"system.":[135],"On":[136],"transitive":[138],"graph,":[139],"naturally":[142],"gives":[143],"upper":[145,185,235],"bound":[146,186,236],"one":[152],"half":[153],"grand":[156],"coupling":[157],"sharp":[161,234],"Ising":[164],"model.":[165],"However,":[166],"many":[168],"systems":[170],"including":[171],"model,":[174],"this":[175,241],"misses":[176],"additional":[177,230],"averaging":[178],"over":[179,214],"update":[181],"histories":[182,205],"giving":[183],"off":[189],"constant":[192],"multiplicate":[193],"factor.":[194],"develop":[196],"new":[198],"framework":[199],"treats":[201],"as":[206],"random":[207],"polymers":[208],"show":[210],"how":[211],"average":[213],"them":[215],"give":[217],"effective":[219],"condition.":[224],"accounts":[226],"all":[228],"mixing,":[231],"recovering":[232],"cutoff.":[238],"believe":[240],"approach":[242],"will":[243],"be":[244],"applicable":[245],"much":[248],"wider":[249],"range":[250],"settings.":[252]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-29T00:00:00"}
