{"id":"https://openalex.org/W7154459609","doi":"https://doi.org/10.48550/arxiv.2604.11938","title":"Sampling Colorings Close to the Maximum Degree: Non-Markovian Coupling and Local Uniformity","display_name":"Sampling Colorings Close to the Maximum Degree: Non-Markovian Coupling and Local Uniformity","publication_year":2026,"publication_date":"2026-04-13","ids":{"openalex":"https://openalex.org/W7154459609","doi":"https://doi.org/10.48550/arxiv.2604.11938"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.11938","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11938","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":"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.11938","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133688810","display_name":"Vishesh Jain","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jain, Vishesh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114353705","display_name":"Clayton Mizgerd","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mizgerd, Clayton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5051363868","display_name":"Eric Vigoda","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vigoda, Eric","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9980999827384949,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.00019999999494757503,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.00019999999494757503,"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/glauber","display_name":"Glauber","score":0.8795999884605408},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.714900016784668},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.5877000093460083},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5296000242233276},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.5029000043869019},{"id":"https://openalex.org/keywords/rejection-sampling","display_name":"Rejection sampling","score":0.47620001435279846},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45719999074935913},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4526999890804291},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4474000036716461},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4189999997615814}],"concepts":[{"id":"https://openalex.org/C2780708879","wikidata":"https://www.wikidata.org/wiki/Q5567254","display_name":"Glauber","level":3,"score":0.8795999884605408},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.714900016784668},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6362000107765198},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.5877000093460083},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5296000242233276},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.5029000043869019},{"id":"https://openalex.org/C187192777","wikidata":"https://www.wikidata.org/wiki/Q381699","display_name":"Rejection sampling","level":5,"score":0.47620001435279846},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45719999074935913},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4526999890804291},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4474000036716461},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4474000036716461},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4429999887943268},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4189999997615814},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.4147000014781952},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37139999866485596},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.36640000343322754},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.36579999327659607},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.3610000014305115},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.3497999906539917},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.28600001335144043},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28130000829696655},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2786000072956085},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2727999985218048},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C170593435","wikidata":"https://www.wikidata.org/wiki/Q4128565","display_name":"Slice sampling","level":4,"score":0.2581999897956848},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C204693719","wikidata":"https://www.wikidata.org/wiki/Q910810","display_name":"Metropolis\u2013Hastings algorithm","level":4,"score":0.2540999948978424},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.11938","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11938","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.11938","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11938","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":"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Sampling":[0],"graph":[1,31,129],"colorings":[2],"via":[3],"local":[4,218],"Markov":[5,15],"chains":[6],"is":[7,40,82],"a":[8,26,30,61,67,83,142,216,246],"central":[9],"problem":[10,23,86],"in":[11,157,186,254],"approximate":[12],"counting":[13],"and":[14,65,108,134,148,166,190,214,221],"chain":[16,49,237],"Monte":[17],"Carlo":[18],"(MCMC).":[19],"We":[20,102,208],"address":[21],"the":[22,46,52,76,90,116,152,187,194,228,235,250,255,268,272],"of":[24,29,45,123,130,176,249],"sampling":[25],"random":[27,62,68],"$k$-coloring":[28],"with":[32,205],"maximum":[33,135],"degree":[34,136],"$\u0394$.":[35,137],"The":[36],"simplest":[37],"algorithmic":[38],"approach":[39,139],"to":[41,73,87,193,239,263,271],"establish":[42],"rapid":[43],"mixing":[44,95,121,266],"single-site":[47],"update":[48],"known":[50],"as":[51],"Metropolis":[53,229],"Glauber":[54,91,117],"dynamics,":[55,230],"which":[56,158],"at":[57,160,170],"each":[58],"step":[59],"chooses":[60],"vertex":[63],"$v$":[64,72],"proposes":[66],"color":[69],"$c$,":[70],"recoloring":[71],"$c$":[74],"if":[75,112],"resulting":[77],"coloring":[78],"remains":[79],"proper.":[80],"It":[81],"long-standing":[84],"open":[85],"prove":[88,103],"that":[89,104,184],"dynamics":[92,118],"has":[93,119],"polynomial":[94],"time":[96,122,161],"on":[97,127,141,165],"all":[98,109,267],"graphs":[99],"whenever":[100],"$k\\geq\u0394+2$.":[101],"for":[105,151,227,234],"every":[106],"$\u03b4&gt;0$":[107],"$\u0394\\geq":[110],"\u0394_0(\u03b4)$,":[111],"$k\\ge":[113],"(1+\u03b4)\u0394$":[114],"then":[115],"optimal":[120,265],"$O_\u03b4(|V|":[124],"\\log":[125],"|V|)$":[126],"any":[128],"girth":[131],"$\\geq":[132],"11$":[133],"Our":[138],"builds":[140],"non-Markovian":[143,201,219,251],"coupling":[144,252],"introduced":[145],"by":[146,212,222],"Hayes":[147,240],"Vigoda":[149],"(2003)":[150],"large-degree":[153,256],"regime":[154,196],"$\u0394=\u03a9(\\log":[155],"n)$,":[156],"updates":[159,169,202],"$t$":[162],"may":[163,203],"depend":[164],"modify":[167],"proposed":[168],"future":[171],"times.":[172],"A":[173],"complete":[174,247],"analysis":[175,248],"this":[177],"framework":[178,253],"requires":[179],"resolving":[180],"substantial":[181],"technical":[182],"obstacles":[183,211],"remain":[185],"original":[188],"argument,":[189],"extending":[191,231],"it":[192,261],"constant-degree":[195,273],"introduces":[197],"further":[198],"difficulties,":[199],"since":[200],"fail":[204],"constant":[206],"probability.":[207],"overcome":[209],"these":[210,243],"developing":[213],"analyzing":[215],"refined":[217],"coupling,":[220],"establishing":[223],"new":[224],"local-uniformity":[225],"results":[226,233],"prior":[232],"heat-bath":[236],"due":[238],"(2013).":[241],"Together,":[242],"ingredients":[244],"provide":[245],"regime,":[257],"while":[258],"simultaneously":[259],"strengthening":[260],"substantially":[262],"obtain":[264],"way":[269],"down":[270],"setting.":[274]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-16T00:00:00"}
