{"id":"https://openalex.org/W2130594164","doi":"https://doi.org/10.1109/tit.1987.1057385","title":"Conditional limit theorems under Markov conditioning","display_name":"Conditional limit theorems under Markov conditioning","publication_year":1987,"publication_date":"1987-11-01","ids":{"openalex":"https://openalex.org/W2130594164","doi":"https://doi.org/10.1109/tit.1987.1057385","mag":"2130594164"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1987.1057385","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1987.1057385","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5026417214","display_name":"Imre Csisz\u00e1r","orcid":"https://orcid.org/0000-0003-1936-2012"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU","US"],"is_corresponding":false,"raw_author_name":"I. Csiszar","raw_affiliation_strings":["Department of Electrical Engineering, University of Maryland, College park, MD, USA","Mathematical Institute of the Hungarian Academy of Sciences, L. E\u00f6tv\u00f6s University, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Maryland, College park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Mathematical Institute of the Hungarian Academy of Sciences, L. E\u00f6tv\u00f6s University, Budapest, Hungary","institution_ids":["https://openalex.org/I7597260","https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055073921","display_name":"Thomas M. Cover","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Cover","raw_affiliation_strings":["Departments of Electrical Engineering and Statistics, University of Stanford, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Electrical Engineering and Statistics, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110079883","display_name":"ByoungSeon Choi","orcid":null},"institutions":[{"id":"https://openalex.org/I193775966","display_name":"Yonsei University","ror":"https://ror.org/01wjejq96","country_code":"KR","type":"education","lineage":["https://openalex.org/I193775966"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Byoung-Seon Choi","raw_affiliation_strings":["Department of Applied Statistics, Yonsei University, Seoul, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Statistics, Yonsei University, Seoul, South Korea","institution_ids":["https://openalex.org/I193775966"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9709,"has_fulltext":false,"cited_by_count":103,"citation_normalized_percentile":{"value":0.91300981,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"33","issue":"6","first_page":"788","last_page":"801"},"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":0.9990000128746033,"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":0.9990000128746033,"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":0.9987000226974487,"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/T11720","display_name":"Probability and Risk Models","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41151198744773865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36508941650390625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35963666439056396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.355544775724411},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35516923666000366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3008069694042206}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41151198744773865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36508941650390625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35963666439056396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.355544775724411},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35516923666000366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3008069694042206}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1987.1057385","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1987.1057385","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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":21,"referenced_works":["https://openalex.org/W148564650","https://openalex.org/W1549664537","https://openalex.org/W1991315500","https://openalex.org/W2010584937","https://openalex.org/W2012867143","https://openalex.org/W2041537137","https://openalex.org/W2046479560","https://openalex.org/W2055094761","https://openalex.org/W2057364883","https://openalex.org/W2058983850","https://openalex.org/W2067596307","https://openalex.org/W2078645667","https://openalex.org/W2087686387","https://openalex.org/W2093716762","https://openalex.org/W2136144249","https://openalex.org/W2160709761","https://openalex.org/W2904772602","https://openalex.org/W4243316134","https://openalex.org/W4246098931","https://openalex.org/W4300614234","https://openalex.org/W6606084189"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Let":[0],"<tex":[1,16,33,42,54,61,67,75,80,96,108,115,132,138,149,153,173],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,17,34,43,55,62,68,76,81,97,109,116,133,139,150,154,174],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X_{1},X_{2},\\cdots</tex>":[3],"be":[4],"independent":[5],"identically":[6],"distributed":[7],"random":[8],"variables":[9],"taking":[10],"values":[11],"in":[12,107,120],"a":[13,52,65,103],"finite":[14],"set":[15],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X</tex>":[18],"and":[19,45,79,183],"consider":[20],"the":[21,26,31,39,46,95],"conditional":[22,87,167],"joint":[23,88,100],"distribution":[24,89,101,131,148],"of":[25,30,51,102],"first":[27],"m":[28,94],"elements":[29],"sample":[32,49],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X_{1},\\cdots":[35],",":[36,57,85,135,145],"X_{n}</tex>":[37],"on":[38,60,152],"condition":[40],"that":[41],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X_{1}=x_{1}</tex>":[44],"sliding":[47],"block":[48],"average":[50],"function":[53],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">h(\\cdot":[56],"\\cdot)</tex>":[58,136],"defined":[59],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X^{2}</tex>":[63],"exceeds":[64],"threshold":[66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\alpha":[69],"&gt;":[70],"Eh(X_{1},":[71],"X_{2})</tex>":[72],".":[73],"For":[74],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</tex>":[77,98],"fixed":[78],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n":[82],"\\rightarrow":[83],"\\infty</tex>":[84],"this":[86,161],"is":[90,112,177,187],"shown":[91],"to":[92,114],"converge":[93],"-step":[99],"Markov":[104,126,181],"chain":[105,182],"started":[106],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x_{1}</tex>":[110],"which":[111],"closest":[113],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X_{l},":[117],"X_{2},":[118],"\\cdots</tex>":[119],"Kullback-Leibler":[121],"information":[122],"divergence":[123],"among":[124],"all":[125],"chains":[127],"whose":[128],"two-dimensional":[129],"stationary":[130],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">P(\\cdot":[134],"satisfies":[137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\sum":[140],"P(x,":[141],"y)h(x,":[142],"y)\\geq":[143],"\\alpha</tex>":[144],"provided":[146],"some":[147],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">P</tex>":[151],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X_{2}</tex>":[155],"having":[156],"equal":[157],"marginals":[158],"does":[159],"satisfy":[160],"constraint":[162],"with":[163],"strict":[164],"inequality.":[165],"Similar":[166],"limit":[168],"theorems":[169],"are":[170],"obtained":[171],"when":[172],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X_{1},":[175],"X_{2},\\cdots</tex>":[176],"an":[178],"arbitrary":[179],"finite-order":[180],"more":[184],"general":[185],"conditioning":[186],"allowed.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
