Sums of random Hermitian matrices and an inequality by Rudelson

@article{Oliveira2010SumsOR,
  title={Sums of random Hermitian matrices and an inequality by Rudelson},
  author={R. I. Oliveira},
  journal={Electronic Communications in Probability},
  year={2010},
  volume={15},
  pages={203-212}
}
  • R. I. Oliveira
  • Published 2010
  • Mathematics
  • Electronic Communications in Probability
We give a new, elementary proof of a key inequality used by Rudelson in the derivation of his well-known bound for random sums of rank-one operators. Our approach is based on Ahlswede and Winter's technique for proving operator Chernoff bounds. We also prove a concentration inequality for sums of random matrices of rank one with explicit constants. 
88 Citations
Dimension-free tail inequalities for sums of random matrices
  • 21
  • PDF
User-Friendly Tail Bounds for Sums of Random Matrices
  • J. Tropp
  • Mathematics, Computer Science
  • Found. Comput. Math.
  • 2012
  • 1,252
  • Highly Influenced
  • PDF
Tail inequalities for sums of random matrices that depend on the intrinsic dimension
  • 62
  • Highly Influenced
  • PDF
User-Friendly Tail Bounds for Matrix Martingales
  • 38
  • PDF
The spectral norm of Gaussian matrices with correlated entries
  • PDF
Sums of Matrix-Valued Random Variables
  • 3
Advanced Tools from Probability Theory
  • 1
Estimating the covariance of random matrices
  • 6
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 24 REFERENCES
On singular values of matrices with independent rows
  • 49
  • PDF
Strong converse for identification via quantum channels
  • 392
  • Highly Influential
  • PDF
LOWER BOUNDS FOR THE HELMHOLTZ FUNCTION
  • 199
Inequality with Applications in Statistical Mechanics
  • 198
  • PDF
Spectral norm of products of random and deterministic matrices
  • 57
  • PDF
Random Vectors in the Isotropic Position
  • 341
  • PDF
Random Cayley Graphs are Expanders: a Simple Proof of the Alon-Roichman Theorem
  • 45
  • PDF
On the conditioning of random subdictionaries
  • 212
  • PDF
...
1
2
3
...