Coverings of random ellipsoids, and invertibility of matrices with i.i.d. heavy-tailed entries

  title={Coverings of random ellipsoids, and invertibility of matrices with i.i.d. heavy-tailed entries},
  author={Elizaveta Rebrova and Konstantin E. Tikhomirov},
  journal={Israel Journal of Mathematics},
Let A = (aij) be an n × n random matrix with i.i.d. entries such that Ea11 = 0 and Ea112 = 1. We prove that for any δ > 0 there is L > 0 depending only on δ, and a subset N of B2n of cardinality at most exp(δn) such that with probability very close to one we have $$A\left( {B_2^n} \right)\subset\mathop \cup \limits_{y \in A\left( \mathcal{N} \right)} \left( {y + L\sqrt n B_2^n} \right)$$A(B2n)∪y∈A(N)(y+LnB2n). In fact, a stronger statement holds true. As an application, we show that for some L… 
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  • Mathematics, Computer Science
    Journal of Theoretical Probability
  • 2019
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