Tropp, Joel A. (2016) The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach. In: High Dimensional Probability VII. Progress in Probability (PRPR). No.71. Springer , Cham, pp. 173-202. ISBN 978-3-319-40517-9. https://resolver.caltech.edu/CaltechAUTHORS:20170214-075417526
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Abstract
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the random matrix and the expectation of the maximum squared norm achieved by one of the summands; there is also a weak dependence on the dimension of the random matrix. The purpose of this paper is to give a complete, elementary proof of this important inequality.
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| Additional Information: | © 2016 Springer International Publishing Switzerland. First Online: 22 September 2016. The author wishes to thank Ryan Lee for a careful reading of the manuscript. The author gratefully acknowledges support from ONR award N00014-11-1002 and the Gordon & Betty Moore Foundation. | |||||||||||||||
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| Subject Keywords: | Probability inequality; Random matrix; Sum of independent random variables | |||||||||||||||
| Series Name: | Progress in Probability (PRPR) | |||||||||||||||
| Issue or Number: | 71 | |||||||||||||||
| Classification Code: | Mathematics Subject Classification (2010): 60B20; 60F10, 60G50, 60G42 | |||||||||||||||
| DOI: | 10.1007/978-3-319-40519-3_8 | |||||||||||||||
| Record Number: | CaltechAUTHORS:20170214-075417526 | |||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170214-075417526 | |||||||||||||||
| Official Citation: | Tropp J.A. (2016) The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach. In: Houdré C., Mason D., Reynaud-Bouret P., Rosiński J. (eds) High Dimensional Probability VII. Progress in Probability, vol 71. Birkhäuser, Cham | |||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||||||||
| ID Code: | 74289 | |||||||||||||||
| Collection: | CaltechAUTHORS | |||||||||||||||
| Deposited By: | Tony Diaz | |||||||||||||||
| Deposited On: | 14 Feb 2017 18:38 | |||||||||||||||
| Last Modified: | 11 Nov 2021 05:26 |
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