Smallest singular value of sparse random matrices
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Probability bounds on singular values of sparse random matrices; pure mathematics.
This proves mathematical results about sparse random matrices, not research itself.
Pure mathematics on singular values of sparse random matrices.
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 $r$-th moment, $r > 2$, of the corresponding entries.
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The record
- Venue
- Studia Mathematica
- Topic
- Random Matrices and Applications
- Field
- Mathematics
- Canadian institutions
- University of Alberta
- Funders
- —
- Keywords
- MathematicsRandom matrixSingular valueClass (philosophy)CombinatoricsValue (mathematics)Matrix (chemical analysis)Moment (physics)Random variableApplied mathematicsDiscrete mathematicsStatisticsComputer sciencePhysics
- Has abstract in OpenAlex
- yes