Normal approximation for weighted sums under a second-order correlation condition

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.

Original languageEnglish (US)
Pages (from-to)1202-1219
Number of pages18
JournalAnnals of Probability
Issue number3
StatePublished - 2020

Bibliographical note

Funding Information:
Acknowledgments. The authors would like to thank the two referees for careful reading of the manuscript and valuable comments. This work was supported by NSF Grant DMS-1855575, the Simons Foundation and CRC 1283 at Bielefeld University.

Publisher Copyright:
© Institute of Mathematical Statistics, 2020.


  • Normal approximation
  • Sudakov's typical distributions


Dive into the research topics of 'Normal approximation for weighted sums under a second-order correlation condition'. Together they form a unique fingerprint.

Cite this