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- W2949286407 abstract "Let $delta>1$ and $beta>0$ be some real numbers. We prove that there are positive $u,v,N_0$ depending only on $beta$ and $delta$ with the following property: for any $N,n$ such that $Nge max(N_0,delta n)$, any $Ntimes n$ random matrix $A=(a_{ij})$ with i.i.d. entries satisfying $suplimits_{lambdain {mathbb R}}{mathbb P}bigl{|a_{11}-lambda|le 1bigr}le 1-beta$ and any non-random $Ntimes n$ matrix $B$, the smallest singular value $s_n$ of $A+B$ satisfies ${mathbb P}bigl{s_n(A+B)le usqrt{N}bigr}le exp(-vN)$. The result holds without any moment assumptions on distribution of the entries of $A$." @default.
- W2949286407 created "2019-06-27" @default.
- W2949286407 creator A5037104598 @default.
- W2949286407 date "2014-09-29" @default.
- W2949286407 modified "2023-09-27" @default.
- W2949286407 title "The smallest singular value of random rectangular matrices with no moment assumptions on entries" @default.
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