{"id":"https://openalex.org/W1593477701","doi":"https://doi.org/10.23919/ecc.2013.6669845","title":"Ergodicity and class-ergodicity of balanced asymmetric stochastic chains","display_name":"Ergodicity and class-ergodicity of balanced asymmetric stochastic chains","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W1593477701","doi":"https://doi.org/10.23919/ecc.2013.6669845","mag":"1593477701"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2013.6669845","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669845","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5088005378","display_name":"Sadegh Bolouki","orcid":"https://orcid.org/0000-0002-4175-5894"},"institutions":[{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]},{"id":"https://openalex.org/I45683168","display_name":"Polytechnique Montr\u00e9al","ror":"https://ror.org/05f8d4e86","country_code":"CA","type":"education","lineage":["https://openalex.org/I45683168"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sadegh Bolouki","raw_affiliation_strings":["GERAD and Department of Electrical Engineering, 2500 Chemin de Polytechnique, Montreal, Quebec","GERAD & Dept. of Electr. Eng., Ecole Polytehnique de Montreal, Montreal, QC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"GERAD and Department of Electrical Engineering, 2500 Chemin de Polytechnique, Montreal, Quebec","institution_ids":["https://openalex.org/I45683168"]},{"raw_affiliation_string":"GERAD & Dept. of Electr. Eng., Ecole Polytehnique de Montreal, Montreal, QC, Canada","institution_ids":["https://openalex.org/I4210133247","https://openalex.org/I45683168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071517656","display_name":"Roland P. Malham\u00e9","orcid":"https://orcid.org/0000-0002-2809-0891"},"institutions":[{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]},{"id":"https://openalex.org/I45683168","display_name":"Polytechnique Montr\u00e9al","ror":"https://ror.org/05f8d4e86","country_code":"CA","type":"education","lineage":["https://openalex.org/I45683168"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Roland P. Malhame","raw_affiliation_strings":["GERAD and Department of Electrical Engineering, 2500 Chemin de Polytechnique, Montreal, Quebec","GERAD & Dept. of Electr. Eng., Ecole Polytehnique de Montreal, Montreal, QC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"GERAD and Department of Electrical Engineering, 2500 Chemin de Polytechnique, Montreal, Quebec","institution_ids":["https://openalex.org/I45683168"]},{"raw_affiliation_string":"GERAD & Dept. of Electr. Eng., Ecole Polytehnique de Montreal, Montreal, QC, Canada","institution_ids":["https://openalex.org/I4210133247","https://openalex.org/I45683168"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6831,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.91139241,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"221","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9945999979972839,"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/ergodicity","display_name":"Ergodicity","score":0.7788574695587158},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5893042087554932},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5555459260940552},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.52269446849823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49466773867607117},{"id":"https://openalex.org/keywords/strongly-connected-component","display_name":"Strongly connected component","score":0.49311110377311707},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4896612763404846},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.43150511384010315},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41348618268966675},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34196460247039795},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12215927243232727}],"concepts":[{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.7788574695587158},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5893042087554932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5555459260940552},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.52269446849823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49466773867607117},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.49311110377311707},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4896612763404846},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.43150511384010315},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41348618268966675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34196460247039795},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12215927243232727},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.23919/ecc.2013.6669845","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669845","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:publications.polymtl.ca:62912","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/62912/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Communication de conf\u00e9rence"},{"id":"pmh:oai:publications.polymtl.ca:63933","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/63933/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Rapport"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/14","score":0.6600000262260437,"display_name":"Life below water"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1547358136","https://openalex.org/W1603765807","https://openalex.org/W1998692453","https://openalex.org/W2015410655","https://openalex.org/W2028706574","https://openalex.org/W2040069990","https://openalex.org/W2068676854","https://openalex.org/W2091372206","https://openalex.org/W2132374969","https://openalex.org/W2154834860","https://openalex.org/W2165744313","https://openalex.org/W2963490876","https://openalex.org/W3099660372"],"related_works":["https://openalex.org/W2313545085","https://openalex.org/W2381286475","https://openalex.org/W2152685658","https://openalex.org/W3091331701","https://openalex.org/W2392918297","https://openalex.org/W2102951916","https://openalex.org/W3124353475","https://openalex.org/W4287660309","https://openalex.org/W2159790760","https://openalex.org/W4301383227"],"abstract_inverted_index":{"Unconditional":[0],"consensus":[1,7,14,74,138],"is":[2,50,65,78,128],"the":[3,17,24,37,44,54,68,82,106,109,133,142],"property":[4,83,124],"of":[5,16,40,56,59,72,84,88,105,108,125,132],"a":[6,30],"algorithm":[8],"for":[9],"multiple":[10,76],"agents,":[11],"to":[12,81],"produce":[13],"irrespective":[15],"particular":[18],"time":[19,137],"or":[20,75],"state":[21],"at":[22],"which":[23],"agent":[25],"states":[26,46,60],"are":[27],"initialized.":[28],"Under":[29],"weak":[31],"condition,":[32],"so-called":[33,110],"balanced":[34,126],"asymmetry,":[35],"on":[36,103],"sequence":[38],"(An)":[39],"stochastic":[41],"matrices":[42],"in":[43,141],"agents":[45],"update":[47],"algorithm,":[48],"it":[49],"shown":[51],"that":[52],"(i)":[53],"set":[55],"accumulation":[57],"points":[58],"as":[61,91,117],"n":[62],"grows":[63],"large":[64],"finite,":[66],"(ii)":[67],"asymptotic":[69],"unconditional":[70],"occurrence":[71],"single":[73],"consensuses":[77],"directly":[79],"related":[80],"absolute":[85],"infinite":[86],"flow":[87],"this":[89],"sequence,":[90],"introduced":[92],"by":[93,115,119,130],"Touri":[94],"and":[95],"Nedi\u0107.":[96],"The":[97,123],"latter":[98],"condition":[99],"must":[100],"be":[101],"satisfied":[102,129],"each":[104],"islands":[107],"unbounded":[111],"interactions":[112],"graph":[113],"induced":[114],"(An),":[116],"defined":[118],"Hendrickx":[120],"et":[121],"al.":[122],"asymmetry":[127],"many":[131],"well":[134],"known":[135],"discrete":[136],"models":[139],"studied":[140],"literature.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}