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Banaszczyk W., Litvak A.E., Pajor A., Szarek S.J. (1999) The flatness theorem for non-symmetric convex bodies via the local theory of Banach spaces. Math. Oper. Res. 24(3):728–750
Barthe F. (1998) An extremal property of the mean width of the simplex. Math. Ann. 310(4):685–693
Benyamini Y., Gordon Y. (1981) Random factorization of operators between Banach spaces. J. Anal. Math. 39:45–74
Bourgain J., Milman V.D. (1986) Distances between normed spaces, their subspaces and quotient spaces. Integral Equations Operator Theory 9:31–46
Bourgain J., Szarek S.J. (1988) The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factorization. Israel J. Math. 62(2):169–180
Giannopoulos A.A. (1995) A note on the Banach-Mazur distance to the cube. In: Geometric Aspects of Functional Analysis (Israel, 1992–1994), Oper. Theory Adv. Appl., 77, Birkhäuser, Basel, 67–73
Gordon Y. (1988) On Milman's inequality and random subspaces which escape through a mesh in ℝn. In: Geometric Aspects of Functional Analysis (1986/87), Lecture Notes in Math., 1317, Springer, Berlin-New York, 84–106
Gordon Y., Guédon O., Meyer M. (1998) An isomorphic Dvoretzky's theorem for convex bodies. Studia Math. 127(2):191–200
Grünbaum B. (1963) Measures of symmetry for convex sets. Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 233–270
Guédon O. (1998) Sections euclidiennes des corps convexes et inégalités de concentration volumique. Thèse de doctorat de mathématiques, Université de Marne-la-Vallée
Johnson W.B., Lindenstrauss J. Extensions of Lipschitz mappings into a Hilbert space. In: Conference in Modern Analysis and Probability (New Haven, Conn., 1982), 189–206
Litvak A.E., Milman V.D., Pajor A. (1999) The covering numbers and “low M*-estimate” for quasi-convex bodies. Proc. Amer. Math. Soc. 127:1499–1507
Mankiewicz P., Tomczak-Jaegermann N. (1990) Pathological properties and dichotomies for random quotients of finite-dimensional Banach spaces. In: Geometry of Banach Spaces (Strobl, 1989), London Math. Soc. Lecture Note Ser., 158, Cambridge Univ. Press, Cambridge, 199–217
Milman V.D. (1985) Almost Euclidean quotient spaces of subspaces of a finite dimensional normed space. Proc. Amer. Math. Soc. 94:445–449
Milman V.D. (1985) Random subspaces of proportional dimension of finite dimensional normed spaces: approach through the isoperimetric inequality. In: Banach Spaces (Columbia, Mo., 1984), Lecture Notes in Math., 1166, Springer, Berlin-New York, 106–115
Milman V.D. (1990) A note on a low M*-estimate. In: Geometry of Banach Spaces (Strobl, 1989), London Math. Soc. Lecture Note Ser., 158, Cambridge Univ. Press, Cambridge, 219–229
Milman V.D. (1991) Some applications of duality relations. Geometric Aspects of Functional Analysis (1989–90), Lecture Notes in Math., 1469, Springer, Berlin, 13–40
Milman V.D., Pajor A. Entropy and asymptotic geometry of nonsymmetric convex bodies. Advances in Math., to appear; see also (1999) Entropy methods in asymptotic convex geometry. C.R. Acad. Sci. Paris, S.I. Math., 329(4):303–308
Milman V.D., Schechtman G. (1985) Asymptotic theory of finite-dimensional normed spaces. Lecture Notes in Math., 1200, Springer, Berlin-New York
Milman V.D., Schechtman G. (1995) An “isomorphic” version of Dvoretzky's theorem. C. R. Acad. Sci. Paris Sr. I Math. 321:541–544
Milman V.D., Schechtman G. (1999) An “isomorphic” version of Dvoretzky's theorem, II. In: Convex Geometric Analysis (Berkeley, CA, 1996), Math. Sci. Res. Inst. Publ., 34, Cambridge Univ. Press, Cambridge, 159–164
Pajor A., Tomczak-Jaegermann N. (1985) Remarques sur les nombres d'entropie d'un opérateur et de son transposé. C. R. Acad. Sci. Paris Sr. I Math. 301(15):743–746
Pajor A., Tomczak-Jaegermann N. (1986), Subspaces of small codimension of finite-dimensional Banach spaces. Proc. Amer. Math. Soc. 97(4):637–642
Pajor A., Tomczak-Jaegermann N. (1989) Volume ratio and other s-numbers of operators related to local properties of Banach spaces. J. Funct. Anal. 87(2):273–293
Palmon O. (1992) The only convex body with extremal distance from the ball is the simplex. Israel J. Math. 80(3):337–349
Pisier G. (1989) The Volume of Convex Bodies and Banach Space Geometry. Cambridge University Press, Cambridge
Rudelson M. Sections of the difference body. Discrete and Computational Geometry, to appear
Rudelson M. Distances between non-symmetric convex bodies and the MM*-estimate. Positivity, to appear
Szarek S.J., Talagrand M. (1989) An “isomorphic” version of the Sauer-Shelah lemma and the Banach-Mazur distance to the cube. In: Geometric Aspects of Functional Analysis (1987–88), Lecture Notes in Math., 1376, Springer, Berlin-New York, 105–112
Tomczak-Jaegermann N. (1989) Banach-Mazur distances and finite-dimensional operator ideals. Pitman Monographs and Surveys in Pure and Applied Mathematics, 38. Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York
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Litvak, A.E., Tomczak-Jaegermann, N. (2000). Random aspects of high-dimensional convex bodies. In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107214
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