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arXiv · 1501.01649

Weak and strong moments of l_r-norms of log-concave vectors

Rafał Latała·Marta Strzelecka
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Abstract

We show that for $p\geq 1$ and $r\geq 1$ the $p$-th moment of the $l_r$-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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Rafał Latała, Marta Strzelecka. 2015-11-02. Weak and strong moments of l_r-norms of log-concave vectors. https://doi.org/10.1090/proc%2F13003

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