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Note on sampling without replacing from a finite collection of matrices
| العنوان: | Note on sampling without replacing from a finite collection of matrices |
|---|---|
| المؤلفون: | Gross, David, Nesme, Vincent |
| سنة النشر: | 2010 |
| المجموعة: | Computer Science Mathematics Quantum Physics |
| مصطلحات موضوعية: | Computer Science - Information Theory, Quantum Physics |
| الوصف: | 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. Comment: 3 pages. Answers a question raised in arXiv:0910.1879. v2: minus one typo. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1001.2738 |
| رقم الانضمام: | edsarx.1001.2738 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |