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Published February 24, 2016 | Submitted
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Equivalence of concentration inequalities for linear and non-linear functions


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.

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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