Rényi divergence and the central limit theorem

S. G. Bobkov, G. P. Chistyakov, F. Götze

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We explore properties of the χ 2 and Rényi distances to the normal law and in particular propose necessary and sufficient conditions under which these distances tend to zero in the central limit theorem (with exact rates with respect to the increasing number of summands).

Original languageEnglish (US)
Pages (from-to)270-323
Number of pages54
JournalAnnals of Probability
Issue number1
StatePublished - Jan 1 2019

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2019.


  • Central limit theorem
  • Rényi and Tsallis entropies
  • χ -divergence


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