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- W2806426664 abstract "Let $A=(a_{ij})$ be an $ntimes n$ random matrix with i.i.d. entries such that $mathbb{E} a_{11} = 0$ and $mathbb{E} {a_{11}}^2 = 1$. We prove that for any $delta>0$ there is $L>0$ depending only on $delta$, and a subset $mathcal{N}$ of $B_2^n$ of cardinality at most $exp(delta n)$ such that with probability very close to one we have $$A(B_2^n)subset bigcup_{yin A(mathcal{N})}bigl(y+Lsqrt{n}B_2^nbigr).$$ As an application, we show that for some $L'>0$ and $uin[0,1)$ depending only on the distribution law of $a_{11}$, the smallest singular value $s_n$ of the matrix $A$ satisfies $mathbb{P}{s_n(A)le varepsilon n^{-1/2}}le L'varepsilon+u^n$ for all $varepsilon>0$. The latter result generalizes a theorem of Rudelson and Vershynin which was proved for random matrices with subgaussian entries." @default.
- W2806426664 created "2018-06-13" @default.
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- W2806426664 date "2015-08-26" @default.
- W2806426664 modified "2023-09-27" @default.
- W2806426664 title "Refined {epsilon}-nets and invertibility of random square matrices with i.i.d. heavy-tailed entries" @default.
- W2806426664 hasPublicationYear "2015" @default.
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