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On Concentration Functions of Random Variables

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Abstract

Concentration functions are considered for sums of independent random variables. Two-sided bounds are given for concentration functions in the case of log-concave distributions.

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Acknowledgments

We thank A. Zaitsev for reading the manuscript. Many thanks to the referee for careful reading, corrections, and helpful comments.

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Authors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Sergey G. Bobkov

  2. University of Bielefeld, Bielefeld, Germany

    Gennadiy P. Chistyakov

Authors
  1. Sergey G. Bobkov
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  2. Gennadiy P. Chistyakov
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Correspondence to Sergey G. Bobkov.

Additional information

Research partially supported by NSF grant DMS-1106530, Simons Fellowship, and SFB 701.

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Bobkov, S.G., Chistyakov, G.P. On Concentration Functions of Random Variables. J Theor Probab 28, 976–988 (2015). https://doi.org/10.1007/s10959-013-0504-1

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  • DOI: https://doi.org/10.1007/s10959-013-0504-1

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