# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

## $\psi _{\alpha }$-estimates for marginals of log-concave probability measuresHTML articles powered by AMS MathViewer

by A. Giannopoulos, G. Paouris and P. Valettas
Proc. Amer. Math. Soc. 140 (2012), 1297-1308 Request permission

## Abstract:

We show that a random marginal $\pi _F(\mu )$ of an isotropic log-concave probability measure $\mu$ on $\mathbb R^n$ exhibits better $\psi _{\alpha }$-behavior. For a natural variant $\psi _{\alpha }^{\prime }$ of the standard $\psi _{\alpha }$-norm we show the following:

1. [(i)] If $k\leq \sqrt {n}$, then for a random $F\in G_{n,k}$ we have that $\pi _F(\mu )$ is a $\psi _2^{\prime }$-measure. We complement this result by showing that a random $\pi _F(\mu )$ is, at the same time, super-Gaussian.

2. [(ii)] If $k=n^{\delta }$, $\frac {1}{2}<\delta <1$, then for a random $F\in G_{n,k}$ we have that $\pi _F(\mu )$ is a $\psi _{\alpha (\delta )}^{\prime }$-measure, where $\alpha (\delta )=\frac {2\delta }{3\delta -1}$.

Similar Articles
• Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46B07, 52A20
• Retrieve articles in all journals with MSC (2010): 46B07, 52A20
• A. Giannopoulos
• Affiliation: Department of Mathematics, University of Athens, Panepistimioupolis 157 84, Athens, Greece
• Email: apgiannop@math.uoa.gr
• G. Paouris
• Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
• MR Author ID: 671202
• Email: grigoris_paouris@yahoo.co.uk
• P. Valettas
• Affiliation: Department of Mathematics, University of Athens, Panepistimioupolis 157 84, Athens, Greece
• MR Author ID: 957443
• Email: petvalet@math.uoa.gr
• Received by editor(s): July 27, 2010
• Received by editor(s) in revised form: December 24, 2010
• Published electronically: August 3, 2011
• Additional Notes: The second author was partially supported by an NSF grant
• Communicated by: Thomas Schlumprecht