{"id":"https://openalex.org/W4406170495","doi":"https://doi.org/10.1109/tac.2025.3527332","title":"A Perron\u2013Frobenius Theorem for Strongly Aperiodic Stochastic Chains","display_name":"A Perron\u2013Frobenius Theorem for Strongly Aperiodic Stochastic Chains","publication_year":2025,"publication_date":"2025-01-08","ids":{"openalex":"https://openalex.org/W4406170495","doi":"https://doi.org/10.1109/tac.2025.3527332"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3527332","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3527332","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5027620589","display_name":"Rohit Parasnis","orcid":"https://orcid.org/0009-0002-8284-9640"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rohit Parasnis","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA"],"raw_orcid":"https://orcid.org/0009-0002-8284-9640","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075999338","display_name":"Massimo Franceschetti","orcid":"https://orcid.org/0000-0002-4057-8152"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Massimo Franceschetti","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-4057-8152","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036105299","display_name":"Behrouz Touri","orcid":"https://orcid.org/0000-0003-4724-7329"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Behrouz Touri","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA"],"raw_orcid":"https://orcid.org/0000-0003-4724-7329","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00450276,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"7","first_page":"4286","last_page":"4301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":1.0,"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":0.9993000030517578,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/irreducibility","display_name":"Irreducibility","score":0.7248426675796509},{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.7246387004852295},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7130687832832336},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5651726722717285},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5455056428909302},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4804527461528778},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4489445686340332},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4479427635669708},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43006598949432373},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4241946339607239},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.4215899705886841},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30604803562164307},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21693387627601624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09745058417320251}],"concepts":[{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.7248426675796509},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.7246387004852295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7130687832832336},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5651726722717285},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5455056428909302},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4804527461528778},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4489445686340332},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4479427635669708},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43006598949432373},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4241946339607239},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.4215899705886841},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30604803562164307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21693387627601624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09745058417320251},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2025.3527332","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3527332","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7741013738","display_name":null,"funder_award_id":"FA9550-23-1-0057","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W15545185","https://openalex.org/W210876736","https://openalex.org/W562922095","https://openalex.org/W1484739396","https://openalex.org/W1516360205","https://openalex.org/W1522371103","https://openalex.org/W1526397541","https://openalex.org/W1788292158","https://openalex.org/W1851248039","https://openalex.org/W1905235987","https://openalex.org/W1984661256","https://openalex.org/W1985343525","https://openalex.org/W2018800107","https://openalex.org/W2018972907","https://openalex.org/W2062448723","https://openalex.org/W2062747548","https://openalex.org/W2062817484","https://openalex.org/W2066105650","https://openalex.org/W2066636486","https://openalex.org/W2068874164","https://openalex.org/W2083689991","https://openalex.org/W2087471349","https://openalex.org/W2091372206","https://openalex.org/W2120239604","https://openalex.org/W2137435346","https://openalex.org/W2144408773","https://openalex.org/W2148606196","https://openalex.org/W2167575818","https://openalex.org/W2271043021","https://openalex.org/W2289181119","https://openalex.org/W2329923978","https://openalex.org/W2749348574","https://openalex.org/W3026613437","https://openalex.org/W3083024126","https://openalex.org/W3093219665","https://openalex.org/W3123808662","https://openalex.org/W4229640694","https://openalex.org/W4244020992","https://openalex.org/W4249595207","https://openalex.org/W4252047513","https://openalex.org/W4301621763","https://openalex.org/W6608425760"],"related_works":["https://openalex.org/W1630580488","https://openalex.org/W2007170860","https://openalex.org/W2037661079","https://openalex.org/W4319349750","https://openalex.org/W2951407429","https://openalex.org/W2339191433","https://openalex.org/W4246385323","https://openalex.org/W4287817191","https://openalex.org/W4298800952","https://openalex.org/W2039582600"],"abstract_inverted_index":{"We":[0,80],"derive":[1],"a":[2,30,60,83],"generalization":[3],"of":[4,17,25,32,39,86],"the":[5,37,54],"Perron-Frobenius":[6],"theorem":[7],"to":[8,43,74,90],"time-varying":[9,23,44],"row-stochastic":[10],"matrices":[11,45],"as":[12],"follows:":[13],"using":[14],"Kolmogorov's":[15],"concept":[16],"absolute":[18,55],"probability":[19,56],"sequences,":[20],"which":[21],"are":[22],"analogs":[24],"principal":[26],"eigenvectors,":[27],"we":[28,48],"identify":[29],"set":[31],"connectivity":[33],"conditions":[34],"that":[35,50],"generalize":[36],"notion":[38],"irreducibility":[40],"(strong":[41],"connectivity)":[42],"(networks),":[46],"and":[47,68,77,97],"show":[49],"under":[51],"these":[52],"conditions,":[53],"sequence":[57,63],"associated":[58],"with":[59],"given":[61],"matrix":[62],"is":[64],"(a)":[65],"uniformly":[66],"positive":[67],"(b)":[69],"unique.":[70],"Our":[71],"results":[72,89],"apply":[73],"both":[75],"discrete-time":[76],"continuous-time":[78],"settings.":[79],"then":[81],"discuss":[82],"few":[84],"applications":[85],"our":[87],"main":[88],"non-Bayesian":[91],"learning,":[92],"distributed":[93],"optimization,":[94],"opinion":[95],"dynamics,":[96],"averaging":[98],"dynamics":[99],"over":[100],"random":[101],"networks.":[102]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}