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arXiv · 1711.02214

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

Rafał Latała
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Abstract

To any $n$-dimensional random vector $X$ we may associate its $L_p$-centroid body ${\cal Z}_p(X)$ and the corresponding norm. We formulate a conjecture concerning the bound on the ${\cal Z}_p(X)$-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.

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Rafał Latała. 2017-11-06. On ${\cal Z}_p$-norms of random vectors. https://doi.org/10.1007/s10958-019-04252-7

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