{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T18:10:00Z","timestamp":1780337400343,"version":"3.54.1"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,5,27]],"date-time":"2021-05-27T00:00:00Z","timestamp":1622073600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Two-sided bounds are explored for concentration functions and R\u00e9nyi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.<\/jats:p>","DOI":"10.1017\/s096354832100016x","type":"journal-article","created":{"date-parts":[[2021,5,27]],"date-time":"2021-05-27T13:33:16Z","timestamp":1622122396000},"page":"54-72","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":15,"title":["Concentration functions and entropy bounds for discrete log-concave distributions"],"prefix":"10.1017","volume":"31","author":[{"given":"Sergey G.","family":"Bobkov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arnaud","family":"Marsiglietti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Melbourne","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2021,5,27]]},"reference":[{"key":"S096354832100016X_ref19","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT44484.2020.9174465"},{"key":"S096354832100016X_ref12","unstructured":"[12] Kapur, J. N. (1988) Generalised Cauchy and Student\u2019s distributions as maximum-entropy distributions. Proc. Nat. Acad. Sci. India Sect. A 58\u00a0235\u2013246."},{"key":"S096354832100016X_ref18","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1109\/TIT.2018.2877741","article-title":"On the entropy power inequality for the R\u00e9nyi entropy of order [0,1].","volume":"65","author":"Marsiglietti","year":"2019","journal-title":"IEEE Trans. Inform. Theory"},{"key":"S096354832100016X_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90071-9"},{"key":"S096354832100016X_ref16","unstructured":"[16] Madiman, M. , Melbourne, J. and Xu, P. (2017) Rogozin\u2019s convolution inequality for locally compact groups. arXiv:1705.00642"},{"key":"S096354832100016X_ref14","volume-title":"In Geometric Aspects of Functional Analysis: GAFA Israel Seminar (2017\u20132019)","author":"Li","year":"2020"},{"key":"S096354832100016X_ref2","first-page":"100","article-title":"Bounds for the maximum of the density of the sum of independent random variables","volume":"199","author":"Bobkov","year":"2012","journal-title":"(Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov."},{"key":"S096354832100016X_ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2020.3024025"},{"key":"S096354832100016X_ref6","doi-asserted-by":"crossref","unstructured":"[6] Costa, J. , Hero, A. and Vignat, C. (2003) On solutions to multivariate maximum \u03b1-entropy problems. In International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2003, pp. 211\u2013226.","DOI":"10.1007\/978-3-540-45063-4_14"},{"key":"S096354832100016X_ref22","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1214\/aoms\/1177729447","article-title":"A lower bound for a probability moment of any absolutely continuous distribution with finite variance","volume":"23","author":"Moriguti","year":"1952","journal-title":"Ann. Math. Statistics"},{"key":"S096354832100016X_ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2070570"},{"key":"S096354832100016X_ref13","doi-asserted-by":"publisher","DOI":"10.4064\/sm170521-5-8"},{"key":"S096354832100016X_ref3","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1109\/TIT.2014.2383379","article-title":"Entropy power inequality for the R\u00e9nyi entropy.","volume":"61","author":"Bobkov","year":"2015","journal-title":"IEEE Trans. Inform. Theory"},{"key":"S096354832100016X_ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.899484"},{"key":"S096354832100016X_ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2616135"},{"key":"S096354832100016X_ref7","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1051\/ps:2006008","article-title":"Preservation of log-concavity on summation","volume":"10","author":"Johnson","year":"2006","journal-title":"ESAIM Probab. Stat."},{"key":"S096354832100016X_ref17","doi-asserted-by":"crossref","first-page":"2911","DOI":"10.1016\/j.disc.2019.03.002","article-title":"Majorization and R\u00e9nyi entropy inequalities via sperner theory","volume":"342","author":"Madiman","year":"2019","journal-title":"Disc. Math."},{"key":"S096354832100016X_ref5","doi-asserted-by":"crossref","first-page":"7747","DOI":"10.1109\/TIT.2017.2764487","article-title":"Variants of the entropy power inequality","volume":"63","author":"Bobkov","journal-title":"IEEE Trans. Inform. Theory"},{"key":"S096354832100016X_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548315000127"},{"key":"S096354832100016X_ref10","first-page":"1","article-title":"An entropy power inequality for the binomial family","volume":"4","author":"Harremo\u00ebs","year":"2003","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"S096354832100016X_ref26","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1989.tb16434.x"},{"key":"S096354832100016X_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s10959-013-0504-1"},{"key":"S096354832100016X_ref21","volume-title":"Bernoulli sums and R\u00e9nyi entropy inequalities","author":"Madiman","year":"2020"},{"key":"S096354832100016X_ref23","first-page":"414","volume-title":"In Ergebnisse der Mathematik und ihrer Grenzgebiete","author":"Petrov","year":"1975"},{"key":"S096354832100016X_ref9","doi-asserted-by":"crossref","first-page":"3787","DOI":"10.1109\/TIT.2014.2317181","article-title":"A new entropy power inequality for integer-valued random variables","volume":"60","author":"Haghighatshoar","year":"2014","journal-title":"IEEE Trans. Inform. Theory"},{"key":"S096354832100016X_ref24","volume-title":"Limit Theorems for Sums of Independent Random Variables.","volume":"320","author":"Petrov","year":"1987"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354832100016X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T10:38:51Z","timestamp":1639996731000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354832100016X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,27]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["S096354832100016X"],"URL":"https:\/\/doi.org\/10.1017\/s096354832100016x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,27]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}