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Weak and strong moments of $ \ell_r$-norms of log-concave vectors


Authors: Rafał Latała and Marta Strzelecka
Journal: Proc. Amer. Math. Soc. 144 (2016), 3597-3608
MSC (2010): Primary 60E15; Secondary 46B09, 52A38
DOI: https://doi.org/10.1090/proc/13003
Published electronically: February 12, 2016
MathSciNet review: 3503729
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Abstract: We show that for $ p\geq 1$ and $ r\geq 1$ the $ p$-th moment of the $ \ell _r$-norm of a log-concave random vector is comparable to the sum of the first moment and the weak $ p$-th moment up to a constant proportional to $ r$. This extends the previous result of Paouris concerning Euclidean norms.


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Additional Information

Rafał Latała
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Email: rlatala@mimuw.edu.pl

Marta Strzelecka
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Email: m.strzelecka@mimuw.edu.pl

DOI: https://doi.org/10.1090/proc/13003
Received by editor(s): January 9, 2015
Received by editor(s) in revised form: October 20, 2015
Published electronically: February 12, 2016
Additional Notes: This research was supported by the NCN grant DEC-2012/05/B/ST1/00412
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2016 American Mathematical Society