Litvak, A;
Rivasplata, O;
(2012)
Smallest singular value of sparse random matrices.
Studia Mathematica
, 212
pp. 195-218.
10.4064/sm212-3-1.
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Abstract
We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances of the entries. We also show that it is enough to require boundedness from above of the rth moment, r > 2, of the corresponding entries.
| Type: | Article |
|---|---|
| Title: | Smallest singular value of sparse random matrices |
| DOI: | 10.4064/sm212-3-1 |
| Publisher version: | http://doi.org/10.4064/sm212-3-1 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| Keywords: | Random matrices, sparse matrices, singular numbers, invertibility of random matrices, subgaussian random variables, compressible and incompressible vectors, deviation inequalities |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10137780 |
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