{"id":"https://openalex.org/W2002240881","doi":"https://doi.org/10.1080/15427951.2006.10129115","title":"Concentration Inequalities and Martingale Inequalities: A Survey","display_name":"Concentration Inequalities and Martingale Inequalities: A Survey","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2002240881","doi":"https://doi.org/10.1080/15427951.2006.10129115","mag":"2002240881"},"language":"en","primary_location":{"id":"doi:10.1080/15427951.2006.10129115","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2006.10129115","pdf_url":"https://www.internetmathematicsjournal.com/article/1413.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.internetmathematicsjournal.com/article/1413.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113657664","display_name":"Fan Chung","orcid":"https://orcid.org/0000-0002-6553-7402"},"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":true,"raw_author_name":"Fan Chung","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, 0012, La Jolla, CA 92093-0112"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, 0012, La Jolla, CA 92093-0112","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036596371","display_name":"Linyuan L\u00fc","orcid":"https://orcid.org/0000-0003-0155-2002"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Linyuan Lu","raw_affiliation_strings":["Department of Mathematics,#N#University of South Carolina,#N#Columbia, SC 29208"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics,#N#University of South Carolina,#N#Columbia, SC 29208","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113657664"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":14.7734,"has_fulltext":false,"cited_by_count":446,"citation_normalized_percentile":{"value":0.99522673,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"3","issue":"1","first_page":"79","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9962000250816345,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.995199978351593,"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/mathematics","display_name":"Mathematics","score":0.8881371021270752},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.7925724387168884},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.6485565900802612},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41253477334976196},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39521169662475586},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3240388035774231},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24616172909736633}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8881371021270752},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.7925724387168884},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.6485565900802612},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41253477334976196},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39521169662475586},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3240388035774231},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24616172909736633},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/15427951.2006.10129115","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2006.10129115","pdf_url":"https://www.internetmathematicsjournal.com/article/1413.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.im/1175266369","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.im/1175266369","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.210.9856","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.9856","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/%7Elu/papers/concen.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.8182","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.8182","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucsd.edu/~fan/wp/concen.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1080/15427951.2006.10129115","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2006.10129115","pdf_url":"https://www.internetmathematicsjournal.com/article/1413.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6100000143051147,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3989395334","display_name":"ITR:   A Twin-Framework To Analyze, Model and Design Robust, Complex Networks Using Biological and Computational Principles","funder_award_id":"0205061","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7961125121","display_name":"Spectral, Extremal & Probabilistic Methods in Graph Theory with Applications to Information Technology","funder_award_id":"0100472","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2002240881.pdf","grobid_xml":"https://content.openalex.org/works/W2002240881.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W123054009","https://openalex.org/W358088974","https://openalex.org/W638149299","https://openalex.org/W1486613786","https://openalex.org/W1591378753","https://openalex.org/W1971289435","https://openalex.org/W1973836644","https://openalex.org/W1993803315","https://openalex.org/W1998475765","https://openalex.org/W2008620264","https://openalex.org/W2027377866","https://openalex.org/W2027939060","https://openalex.org/W2068871408","https://openalex.org/W2077204415","https://openalex.org/W2082137560","https://openalex.org/W2097147952","https://openalex.org/W2103656237","https://openalex.org/W2112643910","https://openalex.org/W2112976607","https://openalex.org/W2124637492","https://openalex.org/W2611932958","https://openalex.org/W2751862591","https://openalex.org/W3110051778","https://openalex.org/W3144881883"],"related_works":["https://openalex.org/W1973641256","https://openalex.org/W2953059741","https://openalex.org/W3007838749","https://openalex.org/W2047131671","https://openalex.org/W2089274067","https://openalex.org/W56994397","https://openalex.org/W2951834733","https://openalex.org/W1121942432","https://openalex.org/W2181432034","https://openalex.org/W4298231342"],"abstract_inverted_index":{"We":[0],"examine":[1],"a":[2],"number":[3],"of":[4,9],"generalized":[5],"and":[6,12,36],"extended":[7],"versions":[8],"concentration":[10],"inequalities":[11,16],"martingale":[13],"inequalities.":[14],"These":[15],"are":[17],"effective":[18],"for":[19,31],"analyzing":[20],"processes":[21],"with":[22],"quite":[23],"general":[24],"conditions":[25],"as":[26],"illustrated":[27],"in":[28],"an":[29,32],"example":[30],"infinite":[33],"Polya":[34],"process":[35],"web":[37],"graphs.":[38]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":48},{"year":2020,"cited_by_count":39},{"year":2019,"cited_by_count":40},{"year":2018,"cited_by_count":35},{"year":2017,"cited_by_count":30},{"year":2016,"cited_by_count":26},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":15}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}
