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A multidimensional analogue of the Rademacher-Gaussian tail comparison


Authors: Piotr Nayar and Tomasz Tkocz
Journal: Proc. Amer. Math. Soc. 146 (2018), 413-419
MSC (2010): Primary 60E15; Secondary 60G15, 60G50
DOI: https://doi.org/10.1090/proc/13731
Published electronically: September 28, 2017
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Abstract: We prove a dimension-free tail comparison between the Euclidean norms of sums of independent random vectors uniformly distributed in centred Euclidean spheres and properly rescaled standard Gaussian random vectors.


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Additional Information

Piotr Nayar
Affiliation: Wharton Statistics Department, University of Pennsylvania, 3730 Walnut Street, Philadelphia, Pennsylvania 19104
Email: nayar@mimuw.edu.pl

Tomasz Tkocz
Affiliation: Department of Mathematics, Fine Hall, Princeton University, Princeton, New Jersey 08544
Email: ttkocz@princeton.edu

DOI: https://doi.org/10.1090/proc/13731
Keywords: Probability inequalities, tail comparison, bounds for tail probabilities, Gaussian random vectors, uniform distributions in Euclidean spheres
Received by editor(s): July 26, 2016
Received by editor(s) in revised form: March 6, 2017
Published electronically: September 28, 2017
Additional Notes: The authors were supported in part by the Simons Foundation. The first author was supported in part by NCN grant DEC-2012/05/B/ST1/00412.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2017 American Mathematical Society

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