On ${\cal Z}_p$-norms of random vectors

Rafał Latała

doi:10.1007/s10958-019-04252-7

paper

On $Z_{p}$ -norms of random vectors

arXiv:1711.02214 · doi:10.1007/s10958-019-04252-7

Abstract

To any $n$ -dimensional random vector $X$ we may associate its $L_{p}$ -centroid body $Z_{p} (X)$ and the corresponding norm. We formulate a conjecture concerning the bound on the $Z_{p} (X)$ -norm of $X$ and show that it holds under some additional symmetry assumptions. We also relate our conjecture with estimates of covering numbers and Sudakov-type minorization bounds.

14 pages

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Abstract

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On $Z_{p}$ -norms of random vectors