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Remarks on the Central Limit Theorem for Non-convex Bodies

Part of the Lecture Notes in Mathematics book series (LNM,volume 2116)

Abstract

In this note, we study possible extensions of the Central Limit Theorem for non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain class of unconditional bodies that are not necessarily convex. Then, we consider a widely-known class of non-convex bodies, the so-called p-convex bodies, and construct a counter-example for this class.

Keywords

  • Classical Central Limit Theorem
  • Unconditional Bodies
  • Berry-Esseen Type Theorem
  • Constant Density Function
  • Haar Probability Measure

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

This paper is part of the authors M.Sc. thesis written under the supervision of Professor Bo’az Klartag whose guidance, support and patience were invaluable. In addition, I would like to thank Andrei Iacob for his helpful editorial comments. Supported by the European Research Council (ERC).

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Correspondence to Uri Grupel .

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Grupel, U. (2014). Remarks on the Central Limit Theorem for Non-convex Bodies. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_14

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