Smallest singular value of sparse random matrices

• Autorzy: Alexander E. Litvak , Omar Rivasplata
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B06: Asymptotic theory of Banach spaces
• 15B52: Random matrices
• 60B20: Random matrices (probabilistic aspects; for algebraic aspects see )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 212
• Numer: 3
• Strony: 195-218

Daty

wydano

2012

Twórcy

autor

Alexander E. Litvak

• Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

autor

Omar Rivasplata

• Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Identyfikatory

DOI

10.4064/sm212-3-1