Geodesic
Smallest singular value of sparse random matrices
Alexander E. Litvak1 ; Omar Rivasplata1
1 Department of Mathematics and Statistical Sciences University of Alberta Edmonton, Alberta T6G 2G1, Canada
Studia Mathematica, Tome 212 (2012) no. 3, pp. 195-218

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $r$th moment, $r > 2$, of the corresponding entries.
DOI : 10.4064/sm212-3-1
Keywords: extend probability estimates smallest singular value random matrices independent entries class sparse random matrices relax previously condition uniform boundedness variances below allows consider matrices null entries generally entries having small variances results assume identical distribution entries random matrix help clarify role variances entries enough require boundedness above rth moment corresponding entries

Alexander E. Litvak 1 ; Omar Rivasplata 1

1 Department of Mathematics and Statistical Sciences University of Alberta Edmonton, Alberta T6G 2G1, Canada 
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Alexander E. Litvak; Omar Rivasplata. Smallest singular value of sparse random matrices. Studia Mathematica, Tome 212 (2012) no. 3, pp. 195-218. doi: 10.4064/sm212-3-1

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