References

• Adamczak, Radosław; Litvak, Alexander E.; Pajor, Alain; Tomczak-Jaegermann, Nicole. Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles. J. Amer. Math. Soc. 23 (2010), no. 2, 535--561. MR2601042
• Adamczak, Radosław; Litvak, Alexander E.; Pajor, Alain; Tomczak-Jaegermann, Nicole. Sharp bounds on the rate of convergence of the empirical covariance matrix. C. R. Math. Acad. Sci. Paris 349 (2011), no. 3-4, 195--200. MR2769907
• Adamczak R., Latala R., Litvak A.E., Pajor A. and Tomczak-Jaegermann N.: Tail estimates for norms of sums of log-concave random vectors, ARXIV1107.4070
• Adamczak, Radosław; Latała, Rafał; Litvak, Alexander E.; Pajor, Alain; Tomczak-Jaegermann, Nicole. Geometry of log-concave ensembles of random matrices and approximate reconstruction. C. R. Math. Acad. Sci. Paris 349 (2011), no. 13-14, 783--786. MR2825941
• Adamczak R., Latala R., Litvak A.E., Oleszkiewicz K., Pajor A. and Tomczak-Jaegermann N.: A short proof of Paouris' inequality, Can. Math. Bull., to appear. ARXIV1205.2515
• Bobkov, Sergey G. Convex bodies and norms associated to convex measures. Probab. Theory Related Fields 147 (2010), no. 1-2, 303--332. MR2594355
• Bobkov, Sergey G. Large deviations and isoperimetry over convex probability measures with heavy tails. Electron. J. Probab. 12 (2007), 1072--1100. MR2336600
• Bobkov, S. G.; Nazarov, F. L. Sharp dilation-type inequalities with fixed parameter of convexity. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 351 (2007), Veroyatnost i Statistika. 12, 54--78, 299; translation in J. Math. Sci. (N. Y.) 152 (2008), no. 6, 826--839 MR2742901
• Bobkov, Sergey; Madiman, Mokshay. Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures. J. Funct. Anal. 262 (2012), no. 7, 3309--3339. MR2885954
• Borell, Christer. Convex measures on locally convex spaces. Ark. Mat. 12 (1974), 239--252. MR0388475
• Borell, C. Convex set functions in $d$-space. Period. Math. Hungar. 6 (1975), no. 2, 111--136. MR0404559
• Borell, Christer. Inverse Hölder inequalities in one and several dimensions. J. Math. Anal. Appl. 41 (1973), 300--312. MR0315073
• Cirelʹson, B. S.; Ibragimov, I. A.; Sudakov, V. N. Norms of Gaussian sample functions. Proceedings of the Third Japan-USSR Symposium on Probability Theory (Tashkent, 1975), pp. 20--41. Lecture Notes in Math., Vol. 550, Springer, Berlin, 1976. MR0458556
• Fradelizi, M. Sections of convex bodies through their centroid. Arch. Math. (Basel) 69 (1997), no. 6, 515--522. MR1480519
• Fradelizi, Matthieu. Concentration inequalities for $s$-concave measures of dilations of Borel sets and applications. Electron. J. Probab. 14 (2009), no. 71, 2068--2090. MR2550293
• Gordon, Yehoram. Some inequalities for Gaussian processes and applications. Israel J. Math. 50 (1985), no. 4, 265--289. MR0800188
• Guédon, Olivier. Kahane-Khinchine type inequalities for negative exponent. Mathematika 46 (1999), no. 1, 165--173. MR1750653
• Guédon, Olivier; Milman, Emanuel. Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures. Geom. Funct. Anal. 21 (2011), no. 5, 1043--1068. MR2846382
• Klartag, B.; Vershynin, R. Small ball probability and Dvoretzky's theorem. Israel J. Math. 157 (2007), 193--207. MR2342445
• Latała, Rafał. Weak and strong moments of random vectors. Marcinkiewicz centenary volume, 115--121, Banach Center Publ., 95, Polish Acad. Sci. Inst. Math., Warsaw, 2011. MR2918093
• Latała, R.; Wojtaszczyk, J. O. On the infimum convolution inequality. Studia Math. 189 (2008), no. 2, 147--187. MR2449135
• Ledoux, Michel. The concentration of measure phenomenon. Mathematical Surveys and Monographs, 89. American Mathematical Society, Providence, RI, 2001. x+181 pp. ISBN: 0-8218-2864-9 MR1849347
• Litvak, A. E.; Milman, V. D.; Schechtman, G. Averages of norms and quasi-norms. Math. Ann. 312 (1998), no. 1, 95--124. MR1645952
• Marshall, Albert W.; Olkin, Ingram; Proschan, Frank. Monotonicity of ratios of means and other applications of majorization. 1967 Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965) pp. 177--190 Academic Press, New York MR0237727
• Mendelson S. and Paouris G.:On the singular values of random matrices, Preprint.
• Milman, V. D.; Pajor, A. Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed $n$-dimensional space. Geometric aspects of functional analysis (1987–88), 64--104, Lecture Notes in Math., 1376, Springer, Berlin, 1989. MR1008717
• Paouris, G. Concentration of mass on convex bodies. Geom. Funct. Anal. 16 (2006), no. 5, 1021--1049. MR2276533
• Paouris, Grigoris. Small ball probability estimates for log-concave measures. Trans. Amer. Math. Soc. 364 (2012), no. 1, 287--308. MR2833584
• Rogers, C. A.; Shephard, G. C. The difference body of a convex body. Arch. Math. (Basel) 8 (1957), 220--233. MR0092172
• Srivastava N. and Vershynin R.: Covariance estimation for distributions with 2+epsilon moments, Ann. of Prob., to appear. ARXIV1106.2775