# Hypercontractivity, and Lower Deviation Estimates in Normed Spaces

@article{Paouris2019HypercontractivityAL, title={Hypercontractivity, and Lower Deviation Estimates in Normed Spaces}, author={Grigoris Paouris and Konstantin E. Tikhomirov and Petros Valettas}, journal={arXiv: Functional Analysis}, year={2019} }

We consider the problem of estimating probabilities of lower deviation $\mathbb P\{\|G\| \leqslant \delta \mathbb E\|G\|\}$ in normed spaces with respect to the Gaussian measure. These estimates occupy central role in the probabilistic study of high-dimensional structures. It has been confirmed in several concrete situations, using ad hoc methods, that lower deviations exhibit very different and more complex behavior than the corresponding upper estimates. A characteristic example of this… Expand

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