Sullivan, T. J. and Owhadi, H.
(2010)
*Equivalence of concentration inequalities for linear and non-linear functions.*
.
(Submitted)
http://resolver.caltech.edu/CaltechAUTHORS:20160224-082333411

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## Abstract

We consider a random variable X that takes values in a (possibly infinite-dimensional) topological vector space X. We show that, with respect to an appropriate "normal distance" on X, concentration inequalities for linear and non-linear functions of X are equivalent. This normal distance corresponds naturally to the concentration rate in classical concentration results such as Gaussian concentration and concentration on the Euclidean and Hamming cubes. Under suitable assumptions on the roundness of the sets of interest, the concentration inequalities so obtained are asymptotically optimal in the high-dimensional limit.

Item Type: | Report or Paper (Discussion Paper) | ||||||
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Additional Information: | (Submitted on 24 Sep 2010). Date: September 27, 2010. The authors acknowledge portions of this work supported by the United States Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through the California Institute of Technology’s ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials. | ||||||

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Subject Keywords: | words and phrases. concentration of measure, large deviations, quasiconvexity, normal distance. | ||||||

Classification Code: | 2010 Mathematics Subject Classification. 60E15, 60F10, 52A07. | ||||||

Record Number: | CaltechAUTHORS:20160224-082333411 | ||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20160224-082333411 | ||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||

ID Code: | 64721 | ||||||

Collection: | CaltechAUTHORS | ||||||

Deposited By: | Ruth Sustaita | ||||||

Deposited On: | 24 Feb 2016 17:55 | ||||||

Last Modified: | 10 Jul 2017 23:59 |

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