{"id":"https://openalex.org/W1926909847","doi":"https://doi.org/10.1137/140987900","title":"Sharp Entrywise Perturbation Bounds for Markov Chains","display_name":"Sharp Entrywise Perturbation Bounds for Markov Chains","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1926909847","doi":"https://doi.org/10.1137/140987900","mag":"1926909847","pmid":"https://pubmed.ncbi.nlm.nih.gov/26491218"},"language":"en","primary_location":{"id":"doi:10.1137/140987900","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140987900","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","pubmed"],"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/A5070853988","display_name":"Erik H. Thiede","orcid":"https://orcid.org/0000-0002-5666-1372"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erik Thiede","raw_affiliation_strings":["The University of Chicago, Department of Chemistry"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Chicago, Department of Chemistry","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057688610","display_name":"Brian Van Koten","orcid":"https://orcid.org/0000-0002-0225-7550"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brian Van Koten","raw_affiliation_strings":["The University of Chicago, Department of Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Chicago, Department of Statistics","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016587955","display_name":"Jonathan Weare","orcid":"https://orcid.org/0000-0001-8745-1821"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan Weare","raw_affiliation_strings":["The University of Chicago, Department of Statistics and the James Franck Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Chicago, Department of Statistics and the James Franck Institute","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":1.0587,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.78503481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"36","issue":"3","first_page":"917","last_page":"941"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994000196456909,"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/T11716","display_name":"Random Matrices and Applications","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7768412232398987},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6894558668136597},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.6789165735244751},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6206941604614258},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5401799082756042},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44276097416877747},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38477444648742676},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3806098997592926},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16774430871009827},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0994507372379303},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09146779775619507},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.08309516310691833}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7768412232398987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6894558668136597},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.6789165735244751},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6206941604614258},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5401799082756042},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44276097416877747},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38477444648742676},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3806098997592926},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16774430871009827},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0994507372379303},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09146779775619507},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08309516310691833},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140987900","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140987900","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"},{"id":"pmid:26491218","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26491218","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on matrix analysis and applications : a publication of the Society for Industrial and Applied Mathematics","raw_type":null},{"id":"pmh:oai:europepmc.org:3583236","is_oa":false,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4610747","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G199968366","display_name":null,"funder_award_id":"R01 GM109455","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W621681426","https://openalex.org/W1500921805","https://openalex.org/W1575147392","https://openalex.org/W1600293573","https://openalex.org/W1972521646","https://openalex.org/W1983161979","https://openalex.org/W1987977794","https://openalex.org/W1992576774","https://openalex.org/W2005325188","https://openalex.org/W2028192443","https://openalex.org/W2058715110","https://openalex.org/W2068042605","https://openalex.org/W2069026191","https://openalex.org/W2081337768","https://openalex.org/W2127255208","https://openalex.org/W2129842602","https://openalex.org/W2132775962","https://openalex.org/W2326968954","https://openalex.org/W2519427475","https://openalex.org/W4239321147"],"related_works":["https://openalex.org/W2734729804","https://openalex.org/W2015136492","https://openalex.org/W2186430569","https://openalex.org/W1968612088","https://openalex.org/W2364963676","https://openalex.org/W3041997070","https://openalex.org/W2735388074","https://openalex.org/W4388292488","https://openalex.org/W2351194865","https://openalex.org/W2756643213"],"abstract_inverted_index":{"For":[0],"many":[1],"Markov":[2],"chains":[3],"of":[4,15,18,30,51,109,125,131],"practical":[5],"interest,":[6],"the":[7,19,48,52,73,78,82,85,90,98,123],"invariant":[8,53,91],"distribution":[9,54,92],"is":[10],"extremely":[11],"sensitive":[12],"to":[13,24,116,128],"perturbations":[14],"some":[16],"entries":[17],"transition":[20,74],"matrix,":[21],"but":[22,119],"insensitive":[23],"others;":[25],"we":[26,65],"give":[27],"an":[28],"example":[29],"such":[31],"a":[32,36,104,126],"chain,":[33],"motivated":[34],"by":[35],"problem":[37],"in":[38,59,97,107],"computational":[39],"statistical":[40],"physics.":[41],"We":[42],"have":[43,103],"derived":[44],"perturbation":[45],"bounds":[46,62,83,96,102],"on":[47,72,77],"relative":[49],"error":[50],"that":[55],"reveal":[56],"these":[57],"variations":[58],"sensitivity.":[60],"Our":[61],"are":[63],"sharp,":[64],"do":[66],"not":[67],"impose":[68],"any":[69],"structural":[70],"assumptions":[71],"matrix":[75],"or":[76,93],"perturbation,":[79],"and":[80],"computing":[81,89,94],"has":[84],"same":[86],"complexity":[87],"as":[88],"other":[95],"literature.":[99],"Moreover,":[100],"our":[101],"simple":[105],"interpretation":[106],"terms":[108],"hitting":[110],"times,":[111],"which":[112],"can":[113],"be":[114],"used":[115],"draw":[117],"intuitive":[118],"rigorous":[120],"conclusions":[121],"about":[122],"sensitivity":[124],"chain":[127],"various":[129],"types":[130],"perturbations.":[132]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}