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• W2963237294 startingPage "1950027" @default.
• W2963237294 abstract "Let [Formula: see text] be an [Formula: see text] random matrix with independent entries and such that in each row entries are i.i.d. Assume also that the entries are symmetric, have unit variances, and satisfy a small ball probabilistic estimate uniformly. We investigate properties of the corresponding random polytope [Formula: see text] in [Formula: see text] (the absolute convex hull of rows of [Formula: see text]). In particular, we show that [Formula: see text] where [Formula: see text] depends only on parameters in small ball inequality. This extends results of [A. E. Litvak, A. Pajor, M. Rudelson and N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005) 491–523] and recent results of [F. Krahmer, C. Kummerle and H. Rauhut, A quotient property for matrices with heavy-tailed entries and its application to noise-blind compressed sensing, preprint (2018); arXiv:1806.04261]. This inclusion is equivalent to so-called [Formula: see text]-quotient property and plays an important role in compressed sensing (see [F. Krahmer, C. Kummerle and H. Rauhut, A quotient property for matrices with heavy-tailed entries and its application to noise-blind compressed sensing, preprint (2018); arXiv:1806.04261] and references therein)." @default.
• W2963237294 created "2019-07-30" @default.
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• W2963237294 date "2019-04-24" @default.
• W2963237294 modified "2023-10-18" @default.
• W2963237294 title "Random polytopes obtained by matrices with heavy-tailed entries" @default.
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• W2963237294 doi "https://doi.org/10.1142/s0219199719500275" @default.
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