Using rademacher permutations to reduce randomness
Algebra i analiz, Tome 19 (2007) no. 1, pp. 23-45.

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It is shown how a special family of unitary operators, called the Rademacher permutations and related to the Clifford algebra, can be used to reduce the level of randomness in several results in asymptotic geometric analysis.
Keywords: Asymptotic geometric analysis, Dvoretzky theorem, concentration, convex body, zigzag body.
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S. Artstein-Avidan; V. D. Milman. Using rademacher permutations to reduce randomness. Algebra i analiz, Tome 19 (2007) no. 1, pp. 23-45. http://geodesic.mathdoc.fr/item/AA_2007_19_1_a1/

[1] Alon N., Spencer J. H., The probabilistic method, Wiley-Intersci. Ser. in Discrete Math. Optim., Wiley-Intersci., New York, 2000 | MR

[2] Artstein-Avidan S., “A Bernstein-Chernoff deviation inequality, and geometric properties of random families of operators”, Israel J. Math., 156 (2006), 187–204 | DOI | MR | Zbl

[3] Artstein-Avidan S., Milman V., “Logarithmic reduction of the level of randomness in some probabilistic geometric constructions”, J. Funct. Anal., 235 (2006), 297–329 | DOI | MR | Zbl

[4] Artstein-Avidan S., Friedland O., Milman V., “Geometric applications of Chernoff-type estimates and a zigzag approximation for balls”, Proc. Amer. Math. Soc., 134 (2006), 1735–1742 | DOI | MR | Zbl

[5] Artstein-Avidan S., Friedland O., Milman V., “Geometric applications of Chernoff-type estimates”, Geometric Aspects of Functional Analysis, Lecture Notes in Math., 1910, Springer, Berlin, 2007, 45–75 | MR | Zbl

[6] Barron A., Cheang G., “A better approximation for balls”, J. Approx. Theory, 104:2 (2000), 183–203 | DOI | MR | Zbl

[7] Ben-Tal A., Nemirovski A., “On polyhedral approximations of the second-order cone”, Math. Oper. Res., 26:2 (2001), 193–205 | DOI | MR | Zbl

[8] Bourgain J., Lindenstrauss J., Milman V., “Minkowski sums and symmetrizations”, Geometric Aspects of Functional Analysis (1986/87), Lecture Notes in Math., 1317, Springer, Berlin, 1988, 44–66 | MR

[9] Giannopoulos A., Milman V., “Euclidean structure in finite dimensional normed spaces”, Handbook of the Geometry of Banach Spaces, Vol. I, North-Holland, Amsterdam, 2001,, 707–779 | MR

[10] Gromov M., Milman V., “A topological application of the isoperimetric inequality”, Amer. J. Math., 105:4 (1983), 843–854 | DOI | MR | Zbl

[11] Milman V., “The concentration phenomenon and linear structure of finite-dimensional normed spaces”, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, CA, 1986), AMS, Providence, RI, 1987, 961–975 | MR

[12] Milman V., Pajor A., “Regularization of star bodies by random hyperplane cut off”, Studia Math., 159:2 (2003), 247–261 | DOI | MR | Zbl

[13] Milman V., Schechtman G., Asymptotic theory of finite-dimensional normed spaces, With an appendix by M. Gromov, Lecture Notes in Math., 1200, Springer-Verlag, Berlin, 1986 | MR | Zbl

[14] Milman V. D., Schechtman G., “Global versus local asymptotic theories of finitedimensional normed spaces”, Duke Math. J., 90:1 (1997), 73–93 | DOI | MR | Zbl

[15] Pisier G., “The volume of convex bodies and Banach space geometry”, Cambridge Tracts in Math., 94 (1989), Cambridge Univ. Press, Cambridge | MR