{"id":"https://openalex.org/W2574088092","doi":"https://doi.org/10.1017/s0963548318000470","title":"Polynomial Mixing of the Edge-Flip Markov Chain for Unbiased Dyadic Tilings","display_name":"Polynomial Mixing of the Edge-Flip Markov Chain for Unbiased Dyadic Tilings","publication_year":2018,"publication_date":"2018-10-31","ids":{"openalex":"https://openalex.org/W2574088092","doi":"https://doi.org/10.1017/s0963548318000470","mag":"2574088092"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548318000470","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548318000470","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://researchportal.bath.ac.uk/en/publications/76332c97-adb3-450c-b0cf-6920fbc45049","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032733831","display_name":"Sarah Cannon","orcid":"https://orcid.org/0000-0001-6510-4669"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. CANNON","raw_affiliation_strings":["Computer Science Division, University of California Berkeley, Berkeley, CA 94720-1776, USA (e-mail:","#N#\u2021#N#Georgia Institute of Technology#N#"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, University of California Berkeley, Berkeley, CA 94720-1776, USA (e-mail:","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"#N#\u2021#N#Georgia Institute of Technology#N#","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065857248","display_name":"David Levin","orcid":"https://orcid.org/0000-0003-1103-6394"},"institutions":[{"id":"https://openalex.org/I181233156","display_name":"University of Oregon","ror":"https://ror.org/0293rh119","country_code":"US","type":"education","lineage":["https://openalex.org/I181233156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. A. LEVIN","raw_affiliation_strings":["Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA (e-mail:","University Of Oregon"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA (e-mail:","institution_ids":["https://openalex.org/I181233156"]},{"raw_affiliation_string":"University Of Oregon","institution_ids":["https://openalex.org/I181233156"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013068717","display_name":"Alexandre Stauffer","orcid":"https://orcid.org/0000-0001-5278-6787"},"institutions":[{"id":"https://openalex.org/I1299528221","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842","country_code":"GB","type":"government","lineage":["https://openalex.org/I1299528221","https://openalex.org/I4210087105"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]},{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"A. STAUFFER","raw_affiliation_strings":["Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK (e-mail:","EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK (e-mail:","institution_ids":["https://openalex.org/I51601045"]},{"raw_affiliation_string":"EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)","institution_ids":["https://openalex.org/I1299528221","https://openalex.org/I4210131439"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032733831"],"corresponding_institution_ids":["https://openalex.org/I130701444","https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":0.7313,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71297517,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"28","issue":"3","first_page":"365","last_page":"387"},"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":0.9987999796867371,"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"}},"topics":[{"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9962000250816345,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9962000250816345,"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/markov-chain","display_name":"Markov chain","score":0.7766692638397217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7384575009346008},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7347300052642822},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.7295176982879639},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.513824999332428},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.5116093754768372},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48874902725219727},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4771527647972107},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.4408310055732727},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43859967589378357},{"id":"https://openalex.org/keywords/markov-chain-mixing-time","display_name":"Markov chain mixing time","score":0.43486297130584717},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4053584039211273},{"id":"https://openalex.org/keywords/markov-property","display_name":"Markov property","score":0.29458069801330566},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24280110001564026},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.22207212448120117},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11939626932144165},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11673220992088318},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1043885350227356},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0980822741985321}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7766692638397217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7384575009346008},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7347300052642822},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.7295176982879639},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.513824999332428},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.5116093754768372},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48874902725219727},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4771527647972107},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.4408310055732727},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43859967589378357},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.43486297130584717},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4053584039211273},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.29458069801330566},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24280110001564026},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.22207212448120117},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11939626932144165},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11673220992088318},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1043885350227356},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0980822741985321},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548318000470","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548318000470","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma3.it:11590/351243","is_oa":false,"landing_page_url":"https://www.scopus.com/inward/record.uri?eid=2-s2.0-85056140355&doi=10.1017%2fS0963548318000470&partnerID=40&md5=22ac3ed7331611f76eae01847a1a3c10","pdf_url":null,"source":{"id":"https://openalex.org/S4377196120","display_name":"Iris (Roma Tre University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119003972","host_organization_name":"Roma Tre University","host_organization_lineage":["https://openalex.org/I119003972"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:purehost.bath.ac.uk:openaire/76332c97-adb3-450c-b0cf-6920fbc45049","is_oa":true,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/76332c97-adb3-450c-b0cf-6920fbc45049","pdf_url":null,"source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cannon, S, Levin, D A & Stauffer, A 2019, 'Polynomial mixing of the edge-flip markov chain for unbiased dyadic tilings', Combinatorics, Probability and Computing, vol. 28, no. 3, pp. 365-387. https://doi.org/10.1017/S0963548318000470","raw_type":"article"},{"id":"pmh:oai:purehost.bath.ac.uk:publications/76332c97-adb3-450c-b0cf-6920fbc45049","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85056140355&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:purehost.bath.ac.uk:openaire/76332c97-adb3-450c-b0cf-6920fbc45049","is_oa":true,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/76332c97-adb3-450c-b0cf-6920fbc45049","pdf_url":null,"source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cannon, S, Levin, D A & Stauffer, A 2019, 'Polynomial mixing of the edge-flip markov chain for unbiased dyadic tilings', Combinatorics, Probability and Computing, vol. 28, no. 3, pp. 365-387. https://doi.org/10.1017/S0963548318000470","raw_type":"article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G282515923","display_name":null,"funder_award_id":"DGE-1650044","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3409049703","display_name":null,"funder_award_id":"EP/N004566/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7798911258","display_name":null,"funder_award_id":"1650044","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1080978","https://openalex.org/W813040336","https://openalex.org/W1600293573","https://openalex.org/W1976418263","https://openalex.org/W1977452791","https://openalex.org/W2000597435","https://openalex.org/W2005219875","https://openalex.org/W2008669237","https://openalex.org/W2010106664","https://openalex.org/W2019620037","https://openalex.org/W2056760934","https://openalex.org/W2062822698","https://openalex.org/W2079416076","https://openalex.org/W2111981124","https://openalex.org/W2134485048","https://openalex.org/W2152646636","https://openalex.org/W2167223378","https://openalex.org/W2167503608","https://openalex.org/W2279676320","https://openalex.org/W2471517265","https://openalex.org/W2570266333","https://openalex.org/W2578911019","https://openalex.org/W2766118105","https://openalex.org/W2886301510","https://openalex.org/W2963129838","https://openalex.org/W2963379837","https://openalex.org/W3105603869","https://openalex.org/W3105703683"],"related_works":["https://openalex.org/W2022929595","https://openalex.org/W3040242514","https://openalex.org/W2792836661","https://openalex.org/W2062240590","https://openalex.org/W2963124996","https://openalex.org/W4310749113","https://openalex.org/W4226280020","https://openalex.org/W222989450","https://openalex.org/W1968605010","https://openalex.org/W1980225355"],"abstract_inverted_index":{"We":[0,174],"give":[1],"the":[2,8,12,44,70,120,141,145,163,180,192,205,208],"first":[3],"polynomial":[4],"upper":[5],"bound":[6,196],"on":[7],"mixing":[9,164],"time":[10,143,165,182],"of":[11,37,43,53,119,144,197,207],"edge-flip":[13,112,146],"Markov":[14,113,147],"chain":[15,114,148],"for":[16,99,149],"unbiased":[17],"dyadic":[18,35,50,60,135,150],"tilings,":[19],"resolving":[20],"an":[21],"open":[22],"problem":[23],"originally":[24],"posed":[25],"by":[26,47,177],"Janson,":[27],"Randall":[28],"and":[29,122],"Spencer":[30],"in":[31,69],"2002":[32],"[14].":[33],"A":[34],"tiling":[36,42,121],"size":[38],"n":[39,48,56,157,171,187,199,201],"is":[40,62,152,166,183],"a":[41,59,73,79,100,116,133],"unit":[45],"square":[46],"non-overlapping":[49],"rectangles,":[51],"each":[52],"area":[54],"1/":[55],",":[57,77,91,101,103,105],"where":[58],"rectangle":[61,64],"any":[63],"that":[65,140,162,179],"can":[66],"be":[67],"written":[68],"form":[71],"[":[72,86],"2":[74,88],"\u2212":[75,82,89,96],"s":[76,83,104],"(":[78,92,156,170],"+":[80,94],"1)2":[81,95],"]":[84,98],"\u00d7":[85],"b":[87,93,102],"t":[90,97,106],"\u2208":[107],"\u2124":[108],"\u2a7e":[109],"0.":[110],"The":[111],"selects":[115],"random":[117],"edge":[118],"replaces":[123],"it":[124],"with":[125],"its":[126],"perpendicular":[127],"bisector":[128],"if":[129],"doing":[130],"so":[131],"yields":[132],"valid":[134],"tiling.":[136],"Specifically,":[137],"we":[138],"show":[139],"relaxation":[142,181],"tilings":[151],"at":[153,167,184],"most":[154,168],"O":[155,169],"4.09":[158],"),":[159,189],"which":[160],"implies":[161],"5.09":[172],").":[173],"complement":[175],"this":[176],"showing":[178],"least":[185],"\u03a9(":[186,198],"1.38":[188],"improving":[190],"upon":[191],"previously":[193],"best":[194],"lower":[195],"log":[200],")":[202],"coming":[203],"from":[204],"diameter":[206],"chain.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}