## Subgaussianity is hereditarily determined

HTML articles powered by AMS MathViewer

- 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 $\{1,\dots ,n\}$.## References

- Sergey G. Bobkov and Fedor L. Nazarov,
*Large deviations of typical linear functionals on a convex body with unconditional basis*, Stochastic inequalities and applications, Progr. Probab., vol. 56, Birkhäuser, Basel, 2003, pp. 3–13. MR**2073422** - Stéphane Boucheron, Gábor Lugosi, and Pascal Massart,
*Concentration inequalities*, Oxford University Press, Oxford, 2013. A nonasymptotic theory of independence; With a foreword by Michel Ledoux. MR**3185193**, DOI 10.1093/acprof:oso/9780199535255.001.0001 - Pandelis Dodos and Vassilis Kanellopoulos,
*Ramsey theory for product spaces*, Mathematical Surveys and Monographs, vol. 212, American Mathematical Society, Providence, RI, 2016. MR**3469779**, DOI 10.1090/surv/212 - John Hancock Elton,
*WEAKLY NULL NORMALIZED SEQUENCES IN BANACH SPACES*, ProQuest LLC, Ann Arbor, MI, 1978. Thesis (Ph.D.)–Yale University. MR**2628434** - John Elton,
*Sign-embeddings of $l^{n}_{1}$*, Trans. Amer. Math. Soc.**279**(1983), no. 1, 113–124. MR**704605**, DOI 10.1090/S0002-9947-1983-0704605-4 - O. Goldreich (editor),
*Property Testing: Current Research and Surveys*, Lecture Notes in Computer Science, Vol. 6390, Springer, 2010. - László Lovász,
*Large networks and graph limits*, American Mathematical Society Colloquium Publications, vol. 60, American Mathematical Society, Providence, RI, 2012. MR**3012035**, DOI 10.1090/coll/060 - Alain Pajor,
*Sous-espaces $l^n_1$ des espaces de Banach*, Travaux en Cours [Works in Progress], vol. 16, Hermann, Paris, 1985 (French). With an introduction by Gilles Pisier. MR**903247** - G. Pisier,
*Subgaussian sequences in probability and Fourier analysis*, Graduate J. Math. 1 (2016), 59–80. (Also available at https://arxiv.org/abs/1607.01053.) - K. F. Roth,
*On certain sets of integers*, J. London Math. Soc.**28**(1953), 104–109. MR**51853**, DOI 10.1112/jlms/s1-28.1.104 - Roman Vershynin,
*High-dimensional probability*, Cambridge Series in Statistical and Probabilistic Mathematics, vol. 47, Cambridge University Press, Cambridge, 2018. An introduction with applications in data science; With a foreword by Sara van de Geer. MR**3837109**, DOI 10.1017/9781108231596

## 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