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Random polytopes: Central limit theorems for intrinsic volumes


Authors: Christoph Thäle, Nicola Turchi and Florian Wespi
Journal: Proc. Amer. Math. Soc. 146 (2018), 3063-3071
MSC (2010): Primary 52A22, 60D05, 60F05
DOI: https://doi.org/10.1090/proc/14000
Published electronically: March 9, 2018
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Abstract: Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimates for floating bodies with Stein's method from probability theory.


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Additional Information

Christoph Thäle
Affiliation: Faculty of Mathematics, Ruhr University, Bochum, Germany
Email: christoph.thaele@rub.de

Nicola Turchi
Affiliation: Faculty of Mathematics, Ruhr University, Bochum, Germany
Email: nicola.turchi@rub.de

Florian Wespi
Affiliation: Institute of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland
Email: florian.wespi@stat.unibe.ch

DOI: https://doi.org/10.1090/proc/14000
Received by editor(s): February 3, 2017
Received by editor(s) in revised form: February 16, 2017, and October 2, 2017
Published electronically: March 9, 2018
Additional Notes: The second author was supported by the Research Training Group RTG 2131 High-dimensional Phenomena in Probability – Fluctuations and Discontinuity.
Communicated by: David Levin
Article copyright: © Copyright 2018 American Mathematical Society

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