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- W2902616427 abstract "Let $Gamma$ be an $Ntimes n$ 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 $Gamma^* B_1^N$ in $mathbb{R}$ (the absolute convex hull of rows of $Gamma$). In particular, we show that $$ Gamma B_1^N supset b^{-1} left( B_{infty}^n cap sqrt{ln (N/n)}, B_2^n right). $$ where $b$ depends only on parameters in small ball inequality. This extends results of cite{LPRT} and recent results of cite{KKR}. This inclusion is equivalent to so-called $ell_1$-quotient property and plays an important role in compressive sensing (see cite{KKR} and references therein)." @default.
- W2902616427 created "2018-12-11" @default.
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- W2902616427 date "2018-11-29" @default.
- W2902616427 modified "2023-09-27" @default.
- W2902616427 title "Random polytopes obtained by matrices with heavy tailed entries" @default.
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- W2902616427 doi "https://doi.org/10.48550/arxiv.1811.12007" @default.
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