{"id":"https://openalex.org/W2169851375","doi":"https://doi.org/10.1109/isit.2010.5513784","title":"R&amp;#x00E9;nyi divergence and majorization","display_name":"R&amp;#x00E9;nyi divergence and majorization","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2169851375","doi":"https://doi.org/10.1109/isit.2010.5513784","mag":"2169851375"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2010.5513784","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513784","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","raw_type":"proceedings-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/A5063805934","display_name":"Tim van Erven","orcid":"https://orcid.org/0000-0002-9200-1451"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Tim van Erven","raw_affiliation_strings":["Centrum Wiskunde and Informatica, Amsterdam, Netherlands"],"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde and Informatica, Amsterdam, Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021606672","display_name":"Peter Harremo\u00ebs","orcid":"https://orcid.org/0000-0002-0441-6690"},"institutions":[{"id":"https://openalex.org/I4210143031","display_name":"Niels Brock","ror":"https://ror.org/03gzqe894","country_code":"DK","type":"education","lineage":["https://openalex.org/I4210143031"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Peter Harremoes","raw_affiliation_strings":["Copenhagen Business College, Copenhagen, Denmark"],"affiliations":[{"raw_affiliation_string":"Copenhagen Business College, Copenhagen, Denmark","institution_ids":["https://openalex.org/I4210143031"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063805934"],"corresponding_institution_ids":["https://openalex.org/I1341640284"],"apc_list":null,"apc_paid":null,"fwci":2.5994,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.91256702,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1335","last_page":"1339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9994999766349792,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9994999766349792,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9678999781608582,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9570000171661377,"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/majorization","display_name":"Majorization","score":0.7084322571754456},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.6964930295944214},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.6954925656318665},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6301043033599854},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.6162844896316528},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.6070602536201477},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5477187633514404},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.5008172988891602},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4877929985523224},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4340240955352783},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3702870011329651},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.20914816856384277},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1731218695640564},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13077419996261597},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06355631351470947}],"concepts":[{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.7084322571754456},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.6964930295944214},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.6954925656318665},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6301043033599854},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.6162844896316528},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.6070602536201477},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5477187633514404},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.5008172988891602},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4877929985523224},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4340240955352783},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3702870011329651},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.20914816856384277},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1731218695640564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13077419996261597},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06355631351470947},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2010.5513784","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513784","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W2006309149","https://openalex.org/W2032916024","https://openalex.org/W2083682556","https://openalex.org/W2086490380","https://openalex.org/W2099111195","https://openalex.org/W2113990831","https://openalex.org/W2122882636","https://openalex.org/W2131940723","https://openalex.org/W2135582882","https://openalex.org/W2165203736","https://openalex.org/W2165730988","https://openalex.org/W3099322555","https://openalex.org/W4300694379"],"related_works":["https://openalex.org/W2920676536","https://openalex.org/W3212925274","https://openalex.org/W3124771927","https://openalex.org/W2385620600","https://openalex.org/W2750125254","https://openalex.org/W4383822431","https://openalex.org/W4367047287","https://openalex.org/W2551182807","https://openalex.org/W4225940264","https://openalex.org/W2509725027"],"abstract_inverted_index":{"R\u00e9nyi":[0,5,33,55,67,85],"divergence":[1,10,14,68,86],"is":[2,18,75],"related":[3,19],"to":[4,20,60,80,98],"entropy":[6],"much":[7],"like":[8],"information":[9,38,46],"(also":[11],"called":[12],"Kullback-Leibler":[13],"or":[15],"relative":[16],"entropy)":[17],"Shannon's":[21],"entropy,":[22],"and":[23],"comes":[24],"up":[25],"in":[26,90],"many":[27],"settings.":[28],"It":[29],"was":[30],"introduced":[31],"by":[32],"as":[34,45],"a":[35,88,103],"measure":[36],"of":[37,54,73,94,102,105],"that":[39],"satisfies":[40],"almost":[41],"the":[42,50,71,78,81,92,100],"same":[43],"axioms":[44],"divergence.":[47],"We":[48,64],"review":[49],"most":[51],"important":[52],"properties":[53],"divergence,":[56],"including":[57],"its":[58],"relation":[59],"some":[61],"other":[62],"distances.":[63],"show":[65],"how":[66],"appears":[69],"when":[70],"theory":[72],"majorization":[74],"generalized":[76],"from":[77],"finite":[79],"continuous":[82],"setting.":[83],"Finally,":[84],"plays":[87],"role":[89],"analyzing":[91],"number":[93],"binary":[95],"questions":[96],"required":[97],"guess":[99],"values":[101],"sequence":[104],"random":[106],"variables.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-13T14:20:09.374765","created_date":"2025-10-10T00:00:00"}
