Asymptotic Behavior of Rényi Entropy in the Central Limit Theorem

Sergey G. Bobkov, Arnaud Marsiglietti

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We explore an asymptotic behavior of Rényi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment hypotheses.

Original languageEnglish (US)
Title of host publicationProgress in Probability
PublisherBirkhauser
Pages169-200
Number of pages32
DOIs
StatePublished - 2019

Publication series

NameProgress in Probability
Volume74
ISSN (Print)1050-6977
ISSN (Electronic)2297-0428

Bibliographical note

Funding Information:
Acknowledgements This research was partially supported by NSF grant DMS-1855575 and BSF grant 2016050. Also, this research was supported in part by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship.

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

  • Central limit theorem
  • Rényi entropy

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