{"id":"https://openalex.org/W2056744345","doi":"https://doi.org/10.1137/0614063","title":"On the Convergence of Reversible Markov Chains","display_name":"On the Convergence of Reversible Markov Chains","publication_year":1993,"publication_date":"1993-10-01","ids":{"openalex":"https://openalex.org/W2056744345","doi":"https://doi.org/10.1137/0614063","mag":"2056744345"},"language":"en","primary_location":{"id":"doi:10.1137/0614063","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614063","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-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/A5033005768","display_name":"Madhav P. Desai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Madhav P. Desai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112780826","display_name":"Vasant B. Rao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vasant B. Rao","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":0.5094,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.64212598,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"4","first_page":"950","last_page":"966"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/markov-chain","display_name":"Markov chain","score":0.8695510029792786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8052527904510498},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.721961498260498},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7144165635108948},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.6191742420196533},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.578530490398407},{"id":"https://openalex.org/keywords/examples-of-markov-chains","display_name":"Examples of Markov chains","score":0.5205539464950562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5195422768592834},{"id":"https://openalex.org/keywords/markov-chain-mixing-time","display_name":"Markov chain mixing time","score":0.507279098033905},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4293630123138428},{"id":"https://openalex.org/keywords/balance-equation","display_name":"Balance equation","score":0.38378384709358215},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37583622336387634},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32942691445350647},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.27559271454811096},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20110595226287842}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.8695510029792786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8052527904510498},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.721961498260498},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7144165635108948},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.6191742420196533},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.578530490398407},{"id":"https://openalex.org/C76408418","wikidata":"https://www.wikidata.org/wiki/Q5419314","display_name":"Examples of Markov chains","level":5,"score":0.5205539464950562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5195422768592834},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.507279098033905},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4293630123138428},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.38378384709358215},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37583622336387634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32942691445350647},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.27559271454811096},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20110595226287842},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0614063","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614063","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W1515707356","https://openalex.org/W1631603072","https://openalex.org/W1983774541","https://openalex.org/W1985318592","https://openalex.org/W1993111701","https://openalex.org/W2005228957","https://openalex.org/W2024060531","https://openalex.org/W2043694962","https://openalex.org/W2072211488","https://openalex.org/W2122141283","https://openalex.org/W2132317856","https://openalex.org/W2165469059","https://openalex.org/W2172129038","https://openalex.org/W2326740504","https://openalex.org/W4299150230"],"related_works":["https://openalex.org/W4235599811","https://openalex.org/W3099350264","https://openalex.org/W4388292488","https://openalex.org/W2100578510","https://openalex.org/W3012090835","https://openalex.org/W84440591","https://openalex.org/W2127370188","https://openalex.org/W1888844679","https://openalex.org/W4231686439","https://openalex.org/W2076033719"],"abstract_inverted_index":{"A":[0],"simple":[1],"upper":[2],"bound":[3,59,74,122],"for":[4,60,90,153],"the":[5,21,24,28,32,42,52,61,76,116,124,140],"second-largest":[6,43],"eigenvalue":[7,63,83],"of":[8,20,31,45,64,79,93,102,127,143],"a":[9,18,39,57,65,73,91,121,128,148],"finite":[10],"reversible":[11,48,66,94,129],"time-homogeneous":[12],"Markov":[13,49,130],"chain":[14,67,131],"is":[15,36,68,147],"presented":[16],"as":[17],"function":[19],"transition":[22],"probabilities,":[23],"equilibrium":[25,135],"distribution,":[26],"and":[27],"underlying":[29,54],"structure":[30],"chain.":[33],"This":[34],"work":[35],"extended":[37],"to":[38,88,120,133],"relation":[40],"between":[41],"eigenvalues":[44,101],"any":[46],"two":[47],"chains":[50,95],"with":[51,106],"same":[53],"structure.":[55],"Furthermore,":[56],"lower":[58],"smallest":[62],"also":[69],"presented,":[70],"thereby":[71],"providing":[72],"on":[75,100,111,115,123],"spectral":[77,117],"gap":[78,118],"such":[80],"chains.":[81],"These":[82],"bounds":[84],"are":[85,158],"fairly":[86],"easy":[87],"compute":[89],"variety":[92],"by":[96],"using":[97],"known":[98],"results":[99,114],"certain":[103],"matrices":[104],"associated":[105],"graphs":[107],"or":[108],"random":[109],"walks":[110],"graphs.":[112],"The":[113],"lead":[119],"time":[125],"constant":[126],"converging":[132],"its":[134],"distribution.":[136],"As":[137],"an":[138],"application,":[139],"temperature":[141],"asymptotics":[142],"simulated":[144],"annealing,":[145],"which":[146],"probabilistic":[149],"algorithm":[150],"widely":[151],"used":[152],"solving":[154],"combinatorial":[155],"optimization":[156],"problems,":[157],"studied.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
