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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Subgaussianity is hereditarily determined
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by Pandelis Dodos and Konstantinos Tyros PDF
Proc. Amer. Math. Soc. 148 (2020), 2915-2930 Request permission

Abstract:

Let $n$ be a positive integer, let $\boldsymbol {X}=(X_1,\dots ,X_n)$ be a random vector in $\mathbb {R}^n$ with bounded entries, and let $(\theta _1,\dots ,\theta _n)$ be a vector in $\mathbb {R}^n$. We show that the subgaussian behavior of the random variable $\theta _1 X_1+\dots +\theta _n X_n$ is essentially determined by the subgaussian behavior of the random variables $\sum _{i\in H} \theta _i X_i$ where $H$ is a random subset of $\{1,\dots ,n\}$.
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Additional Information
  • Pandelis Dodos
  • Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 157 84, Athens, Greece
  • Email: pdodos@math.uoa.gr
  • Konstantinos Tyros
  • Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 157 84, Athens, Greece
  • Email: ktyros@math.uoa.gr
  • Received by editor(s): April 25, 2019
  • Received by editor(s) in revised form: October 29, 2019, and November 6, 2019
  • Published electronically: February 18, 2020
  • Communicated by: Stephen Dilworth
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 2915-2930
  • MSC (2010): Primary 46B09, 60E15
  • DOI: https://doi.org/10.1090/proc/14947
  • MathSciNet review: 4099780