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A simplified proof of CLT for convex bodies


Author: Daniel J. Fresen
Journal: Proc. Amer. Math. Soc. 149 (2021), 345-354
MSC (2010): Primary 52A20, 52A23, 60F05; Secondary 26B25, 52A38, 62E20
DOI: https://doi.org/10.1090/proc/15000
Published electronically: October 1, 2020
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Abstract: We present a short proof of Klartag's central limit theorem for convex bodies, using only the most classical facts about log-concave functions. An appendix is included where we give the proof that the thin shell implies CLT. The paper is accessible to anyone.


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Additional Information

Daniel J. Fresen
Affiliation: Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield, Pretoria 0028, South Africa
Email: daniel.fresen@up.ac.za

DOI: https://doi.org/10.1090/proc/15000
Keywords: Central limit theorem for convex bodies, log-concave function
Received by editor(s): July 19, 2019
Received by editor(s) in revised form: December 7, 2019
Published electronically: October 1, 2020
Additional Notes: Funding received from the University of Pretoria Research Development Programme
Communicated by: Zhen-Qing Chen
Article copyright: © Copyright 2020 American Mathematical Society