# Dichotomies, structure, and concentration in normed spaces

@article{Paouris2018DichotomiesSA, title={Dichotomies, structure, and concentration in normed spaces}, author={Grigoris Paouris and Petros Valettas}, journal={Advances in Mathematics}, year={2018} }

Abstract We use probabilistic, topological and combinatorial methods to establish the following deviation inequality: For any normed space X = ( R n , ‖ ⋅ ‖ ) there exists an invertible linear map T : R n → R n with P ( | ‖ T G ‖ − E ‖ T G ‖ | > e E ‖ T G ‖ ) ≤ C exp ( − c max { e 2 , e } log n ) , e > 0 , where G is the standard n-dimensional Gaussian vector and C , c > 0 are universal constants. It follows that for every e ∈ ( 0 , 1 ) and for every normed space X = ( R n , ‖ ⋅ ‖ ) there…

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