Weak and strong moments of $\ell _r$-norms of log-concave vectors
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- by Rafał Latała and Marta Strzelecka PDF
- Proc. Amer. Math. Soc. 144 (2016), 3597-3608 Request permission
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.References
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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
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3597-3608
- MSC (2010): Primary 60E15; Secondary 46B09, 52A38
- DOI: https://doi.org/10.1090/proc/13003
- MathSciNet review: 3503729