{"id":"https://openalex.org/W1989688866","doi":"https://doi.org/10.1109/isit.2005.1523662","title":"Concentration and relative entropy for compound Poisson distributions","display_name":"Concentration and relative entropy for compound Poisson distributions","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1989688866","doi":"https://doi.org/10.1109/isit.2005.1523662","mag":"1989688866"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2005.1523662","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2005.1523662","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","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/A5089127356","display_name":"Mokshay Madiman","orcid":"https://orcid.org/0000-0002-2992-1829"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. Madiman","raw_affiliation_strings":["Division of Applied Mathematics & Department of Computer Science, Brown University, Providence, RI, USA","Div. of Appl. Math., Brown Univ., Providence, RI"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics & Department of Computer Science, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]},{"raw_affiliation_string":"Div. of Appl. Math., Brown Univ., Providence, RI","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044225058","display_name":"Ioannis Kontoyiannis","orcid":"https://orcid.org/0000-0001-7242-6375"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"I. Kontoyiannis","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI, USA","Div. of Appl. Math., Brown Univ., Providence, RI"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]},{"raw_affiliation_string":"Div. of Appl. Math., Brown Univ., Providence, RI","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089127356"],"corresponding_institution_ids":["https://openalex.org/I27804330"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.10827683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"68","issue":null,"first_page":"1833","last_page":"1837"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9740999937057495,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.6601343154907227},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.6256536245346069},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5578572750091553},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5288211703300476},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5164163708686829},{"id":"https://openalex.org/keywords/concentration-of-measure","display_name":"Concentration of measure","score":0.477232962846756},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.46859636902809143},{"id":"https://openalex.org/keywords/logarithmic-distribution","display_name":"Logarithmic distribution","score":0.45762667059898376},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4225572347640991},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36588406562805176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25026288628578186},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2104858160018921},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15655064582824707},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09510642290115356}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6601343154907227},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.6256536245346069},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5578572750091553},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5288211703300476},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5164163708686829},{"id":"https://openalex.org/C84498859","wikidata":"https://www.wikidata.org/wiki/Q5158327","display_name":"Concentration of measure","level":2,"score":0.477232962846756},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.46859636902809143},{"id":"https://openalex.org/C126506180","wikidata":"https://www.wikidata.org/wiki/Q1867999","display_name":"Logarithmic distribution","level":4,"score":0.45762667059898376},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4225572347640991},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36588406562805176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25026288628578186},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2104858160018921},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15655064582824707},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09510642290115356},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2005.1523662","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2005.1523662","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.","raw_type":"proceedings-article"},{"id":"pmh:oai:generic.eprints.org:960510","is_oa":false,"landing_page_url":"http://publications.eng.cam.ac.uk/960510/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922847","display_name":"Cambridge University Engineering Department Publications Database","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5600000023841858,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1568481205","https://openalex.org/W1573820523","https://openalex.org/W1621813423","https://openalex.org/W1972670046","https://openalex.org/W1973286131","https://openalex.org/W1974349322","https://openalex.org/W1998123258","https://openalex.org/W2014425831","https://openalex.org/W2017077509","https://openalex.org/W2035457377","https://openalex.org/W2044213199","https://openalex.org/W2061328864","https://openalex.org/W2087692101","https://openalex.org/W2098154065","https://openalex.org/W2110814480","https://openalex.org/W2134345656","https://openalex.org/W2144057369","https://openalex.org/W2327680971","https://openalex.org/W2797641211","https://openalex.org/W2950731628","https://openalex.org/W2952247230","https://openalex.org/W3099678718","https://openalex.org/W3102145825","https://openalex.org/W4241684091"],"related_works":["https://openalex.org/W2078434833","https://openalex.org/W2981570916","https://openalex.org/W2191151243","https://openalex.org/W2913782416","https://openalex.org/W1968143934","https://openalex.org/W2000055464","https://openalex.org/W2128715686","https://openalex.org/W1649077467","https://openalex.org/W2904916555","https://openalex.org/W2150461843"],"abstract_inverted_index":{"Using":[0],"a":[1,14,18,54,84,99,121,147],"simple":[2,15],"inequality":[3,20,31],"about":[4],"the":[5,34,67,92,113,139,162,173],"relative":[6],"entropy,":[7],"its":[8,144],"so-called":[9],"\"tensorization":[10],"property,\"":[11],"we":[12,64,136],"give":[13],"proof":[16],"of":[17,36,56,116,172,177],"functional":[19,30],"which":[21],"is":[22,83,164],"satisfied":[23],"by":[24,146],"any":[25],"compound":[26,50,85],"Poisson":[27,51,86],"distribution.":[28],"This":[29,167],"belongs":[32],"to":[33,44,74,130,169],"class":[35],"modified":[37,73],"logarithmic":[38],"Sobolev":[39],"inequalities.":[40],"We":[41],"use":[42],"it":[43],"obtain":[45],"measure":[46],"concentration":[47,77,178],"bounds":[48,179],"for":[49,108],"distributions":[52],"under":[53],"variety":[55],"assumptions":[57],"on":[58,91],"their":[59],"tail":[60],"behavior.":[61],"In":[62],"particular,":[63],"show":[65,137],"how":[66],"celebrated":[68],"\"Herbst":[69],"argument\"":[70],"can":[71],"be":[72,98,170],"yield":[75],"sub-exponential":[76],"bounds.":[78],"For":[79],"example,":[80],"suppose":[81],"Z":[82,117],"random":[87],"variable":[88],"with":[89,180],"values":[90],"nonnegative":[93],"integers,":[94],"and":[95],"let":[96],"f":[97],"function":[100,124],"such":[101],"that":[102,138,141],"|f(k+1)":[103],"-":[104],"f(k)|":[105],"les":[106],"1":[107],"all":[109],"k.":[110],"Then,":[111],"if":[112],"base":[114],"distribution":[115],"does":[118],"not":[119],"have":[120],"finite":[122,127],"moment-generating":[123],"but":[125],"has":[126],"moments":[128],"up":[129],"some":[131],"order":[132],"L":[133],">":[134],"1,":[135],"probability":[140],"f(Z)":[142],"exceeds":[143],"mean":[145],"positive":[148],"amount":[149],"t":[150],"or":[151],"more":[152],"decays":[153],"approximately":[154],"like":[155],"(const)middott":[156],"<sup":[157],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[158],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-L</sup>":[159],",":[160],"where":[161],"constant":[163],"explicitly":[165],"identified.":[166],"appears":[168],"one":[171],"very":[174],"first":[175],"examples":[176],"power-law":[181],"decay":[182]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}