{"id":"https://openalex.org/W2129997211","doi":"https://doi.org/10.1007/11777830_10","title":"On the Convergence Rate of Quasi Lumpable Markov Chains","display_name":"On the Convergence Rate of Quasi Lumpable Markov Chains","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2129997211","doi":"https://doi.org/10.1007/11777830_10","mag":"2129997211"},"language":"en","primary_location":{"id":"doi:10.1007/11777830_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11777830_10","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5009539372","display_name":"Andr\u00e1s Farag\u00f3","orcid":"https://orcid.org/0000-0001-8952-6946"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andr\u00e1s Farag\u00f3","raw_affiliation_strings":["The University of Texas at Dallas, Richardson, Texas, USA"],"affiliations":[{"raw_affiliation_string":"The University of Texas at Dallas, Richardson, Texas, USA","institution_ids":["https://openalex.org/I162577319"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009539372"],"corresponding_institution_ids":["https://openalex.org/I162577319"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.10642093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"138","last_page":"147"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9926000237464905,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9847000241279602,"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/markov-chain","display_name":"Markov chain","score":0.881169855594635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.689387321472168},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6530119180679321},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5486323833465576},{"id":"https://openalex.org/keywords/examples-of-markov-chains","display_name":"Examples of Markov chains","score":0.5456862449645996},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.538651704788208},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5221529006958008},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.481652170419693},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4670872390270233},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4624019265174866},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.4499092400074005},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4440811276435852},{"id":"https://openalex.org/keywords/markov-kernel","display_name":"Markov kernel","score":0.43289482593536377},{"id":"https://openalex.org/keywords/markov-chain-mixing-time","display_name":"Markov chain mixing time","score":0.4189174473285675},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39207813143730164},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37744051218032837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29708266258239746},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18619316816329956},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.12412172555923462},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.10025513172149658},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06723040342330933},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0637444257736206}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.881169855594635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.689387321472168},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6530119180679321},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5486323833465576},{"id":"https://openalex.org/C76408418","wikidata":"https://www.wikidata.org/wiki/Q5419314","display_name":"Examples of Markov chains","level":5,"score":0.5456862449645996},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.538651704788208},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5221529006958008},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.481652170419693},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4670872390270233},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4624019265174866},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.4499092400074005},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4440811276435852},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.43289482593536377},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.4189174473285675},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39207813143730164},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37744051218032837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29708266258239746},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18619316816329956},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.12412172555923462},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.10025513172149658},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06723040342330933},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0637444257736206},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11777830_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11777830_10","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W427836156","https://openalex.org/W1568495775","https://openalex.org/W1985162256","https://openalex.org/W2005711104","https://openalex.org/W2023563854","https://openalex.org/W2048074087","https://openalex.org/W2058837004","https://openalex.org/W2075379212","https://openalex.org/W4213347800","https://openalex.org/W4232461091"],"related_works":["https://openalex.org/W1560931929","https://openalex.org/W4235599811","https://openalex.org/W2100578510","https://openalex.org/W2987631717","https://openalex.org/W2735859191","https://openalex.org/W190459708","https://openalex.org/W50519898","https://openalex.org/W1493775604","https://openalex.org/W2989366387","https://openalex.org/W2949651244"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
