Note on sampling without replacing from a finite collection of matrices
Gross, David ; Nesme, Vincent
arXiv, 1001.2738 / Harvested from arXiv
This technical note supplies an affirmative answer to a question raised in a recent pre-print [arXiv:0910.1879] in the context of a "matrix recovery" problem. Assume one samples m Hermitian matrices X_1, ..., X_m with replacement from a finite collection. The deviation of the sum X_1+...+X_m from its expected value in terms of the operator norm can be estimated by an "operator Chernoff-bound" due to Ahlswede and Winter. The question arose whether the bounds obtained this way continue to hold if the matrices are sampled without replacement. We remark that a positive answer is implied by a classical argument by Hoeffding. Some consequences for the matrix recovery problem are sketched.
Publié le : 2010-01-15
Classification:  Computer Science - Information Theory,  Quantum Physics
@article{1001.2738,
     author = {Gross, David and Nesme, Vincent},
     title = {Note on sampling without replacing from a finite collection of matrices},
     journal = {arXiv},
     volume = {2010},
     number = {0},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1001.2738}
}
Gross, David; Nesme, Vincent. Note on sampling without replacing from a finite collection of matrices. arXiv, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/1001.2738/