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Asymptotic Behavior of Rényi Entropy in the Central Limit Theorem

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High Dimensional Probability VIII

Part of the book series: Progress in Probability ((PRPR,volume 74))

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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.

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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.

Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, USA

    Sergey G. Bobkov

  2. Department of Mathematics, University of Florida, Gainesville, FL, USA

    Arnaud Marsiglietti

Authors
  1. Sergey G. Bobkov
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  2. Arnaud Marsiglietti
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Corresponding author

Correspondence to Arnaud Marsiglietti .

Editor information

Editors and Affiliations

  1. MAP 5, Université Paris Descartes, Paris, France

    Nathael Gozlan

  2. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Rafał Latała

  3. Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, France

    Karim Lounici

  4. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Mokshay Madiman

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Bobkov, S.G., Marsiglietti, A. (2019). Asymptotic Behavior of Rényi Entropy in the Central Limit Theorem. In: Gozlan, N., Latała, R., Lounici, K., Madiman, M. (eds) High Dimensional Probability VIII. Progress in Probability, vol 74. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-26391-1_11

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