Geodesic
Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 85-96 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that the distribution function for the maximum of the modulus of a set $n$ of jointly Gaussian random variables with given variance and zero mean is minimal if these variables are independent. For $n\leqslant N$ let $$ \alpha_{N,n}=\sup_{x_1,\dots,x_N\in B_2^n}\inf_{z\in S^{n-1}}\sup_{1\leqslant j\leqslant N}|\langle x_j,z\rangle|. $$ As a corollary of the result mentioned, the precise orders of the constants $\alpha_{N,n}$ are computed $\alpha_{N,n}\asymp\min\{1,\sqrt{n^{-1}\log(1+N/n)}\}$, and various improvements of these inequalities are obtained. The estimates are used in particular to construct lacunary analogues of the Rudin–Shapiro trigonometric polynomials. Bibliography: 23 titles. 
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     title = {Extremal properties of orthogonal parallelepipeds and their applications to the geometry of {Banach} spaces},
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E. D. Gluskin. Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 85-96. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a4/

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