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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 457, Pages 211–225
(Mi znsl6558)
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This article is cited in 1 scientific paper (total in 1 paper)
On $\mathcal Z_p$-norms of random vectors
R. Latała Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Abstract:
To any $n$-dimensional random vector $X$ we may associate its $L_p$-centroid body $\mathcal Z_p(X)$ and the corresponding norm. We formulate a conjecture concerning the bound on the $\mathcal Z_p(X)$-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 minoration bounds.
Key words and phrases:
$L_p$-centroid body, log-concave distribution, metric entropy, Sudakov minoration.
Received: 29.06.2017
Citation:
R. Latała, “On $\mathcal Z_p$-norms of random vectors”, Probability and statistics. Part 25, Zap. Nauchn. Sem. POMI, 457, POMI, St. Petersburg, 2017, 211–225; J. Math. Sci. (N. Y.), 238:4 (2019), 484–494
Linking options:
https://www.mathnet.ru/eng/znsl6558 https://www.mathnet.ru/eng/znsl/v457/p211
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Abstract page: | 94 | Full-text PDF : | 32 | References: | 28 |
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