Papers by Alexander Litvak

• R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Tail estimates for norms of sums of log-concave random vectors", submitted. PDF, PS.

• R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Chevet type inequality and norms of submatrices", submitted. PDF, PS.

• A. E. Litvak, O. Rivasplata, "Smallest singular value of sparse random matrices", submitted. PDF, PS.

• E. D. Gluskin, A. E. Litvak, "A remark on vertex index of the convex bodies", GAFA, Lecture Notes in Math., Springer, Berlin, to appear. PDF, PS.

• Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "Uniform estimates for order statistics and Orlicz functions", Positivity, 16 (2012), 1--28. PDF, PS.

• R. Adamczak, O. Guedon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Condition number of a square matrix with i.i.d. columns drawn from a convex body", Proc. Amer. Math. Soc., 140 (2012), 987--998. PDF, PS.

• O. Guedon, A. E. Litvak, "On the symmetric average of a convex body", Advances in Geometry, 11 (2011), 615--622. PDF, PS.

• R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Geometry of log-concave Ensembles of random matrices and approximate reconstruction", C.R. Math. Acad. Sci. Paris, 349 (2011), 783--786. PDF, PS.

• R. Adamczak, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Sharp bounds on the rate of convergence of empirical covariance matrix", C.R. Math. Acad. Sci. Paris, 349 (2011), 195--200. PDF, PS.

• R. Adamczak, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling", Constructive Approximation, 34 (2011), 61--88. PDF, PS.

• A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann, "Essentially-Euclidean convex bodies", Studia Math., 196 (2010), 207--221. PDF, PS.

• R. Adamczak, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Quantitative estimates of the convergence of the empirical covariance matrix in Log-concave Ensembles", Journal of AMS, 234 (2010), 535--561. PDF, PS.

• K. Bezdek, A. E. Litvak, "Covering convex bodies by cylinders and lattice points by flats", Journal of Geometric Analysis, 19 (2009). 233--243. PDF, PS.

• R. Adamczak, O. Guedon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Smallest singular value of random matrices with independent columns", C.R. Math. Acad. Sci. Paris, 346 (2008), 853--856. PDF, PS.

• E. D. Gluskin, A. E. Litvak, "Asymmetry of convex polytopes and vertex index of symmetric convex bodies.", Discrete and Computational Geometry, 40 (2008), 528--536. PDF, PS.

• Y. Gordon, A. E. Litvak, S. Mendelson, A. Pajor, "Gaussian averages of interpolated bodies and applications to approximate reconstruction", J. of Approx. Theory, 149 (2007), 59--73. PDF, PS.

• K. Bezdek, A. E. Litvak, "On the vertex index of convex bodies", Adv. Math., 215 (2007), 626--641. PDF, PS.

• A. E. Litvak, V. D. Milman, A. Pajor, N. Tomczak-Jaegermann, "On the Euclidean metric entropy of convex bodies", GAFA, Lecture Notes in Math., 1910, 221--235, Springer, Berlin, 2007. PDF, PS.

• Y. Gordon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Random $\eps$ nets and embeddings in $\ell^N_\infty$", Stud. Math., 178 (2007), 91--98. PDF, PS.

• A. E. Litvak, V. D. Milman, A. Pajor, N. Tomczak-Jaegermann, "Entropy extension", Funct. Anal. Appl., 40 (2006), 298--303. PDF, PS.

• Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "On the minimum of several random variables", Proc. AMS, 134 (2006), 3665--3675. PDF, PS.

• A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Diameters of Sections and Coverings of Convex Bodies", J. of Funct. Anal., 231 (2006), 438--457. PDF, PS.

• A. E. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R. Vershynin, "Euclidean embeddings in spaces of finite volume ratio via random matrices", J. Reine Angew. Math., 589 (2005), 1--19. PDF, PS.

• A. E. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, "Smallest singular value of random matrices and geometry of random polytopes", Adv. Math., 195 (2005), 491--523. PDF, PS.

• Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "Minima of sequences of Gaussian random variables", C.R. Acad. Sci. Paris, Ser 1, Math., 340 (2005), 445--448. PDF, PS.

• A. E. Litvak, "On the dual form of "Low M* -estimate" in the quasi-convex case", Positivity, 8 (2004), 401--406. PDF, PS.

• A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann, "When random proportional subspaces are also random quotients", J. of Funct. Anal., 213 (2004), 270--289. PDF, PS.

• Y. Gordon, A. E. Litvak, M. Meyer, A. Pajor, "John's decomposition in the general case and applications", J. of Diff. Geometry, 68 (2004), 99--119. PDF, PS.

• A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann, "Isomorphic random subspaces and quotients of convex and quasi-convex bodies", GAFA, Lecture Notes in Math., 1850, 159--178, Springer-Verlag, 2004. PDF, PS.

• A. E. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R. Vershynin, "Random Euclidean embeddings in spaces of bounded volume ratio", C.R. Acad. Sci. Paris, Ser 1, Math., 339 (2004), 33--38. PDF, PS.

• A. E. Litvak, V. D. Milman, "Euclidean sections of direct sums of normed spaces", Can. Math. Bull., 46 (2003), 242--251. PDF, PS.

• Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "Geometry of spaces between zonoids and polytopes", Bull. Sci. Math., 126 (2002), 733--762. PDF, PS.

• Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "Orlicz Norms of Sequences of Random Variables", Ann. Probab., 30 (2002), 1833--1853. PDF, PS.

• A. E. Litvak, P. Mankiewicz, N. Tomczak-Jaegermann, "Randomized Isomorphic Dvoretzky Theorem", C.R. Acad. Sci. Paris, Ser 1, Math., 335 (2002), 345--350. PDF, PS.

• N. J. Kalton, A. E. Litvak, "A remark on quotients of finite-dimensional quasi-normed spaces", Houston Journal of Math., 28 (2002), 585--597. PDF, PS.

• E. D. Gluskin, A. E. Litvak, "On the asymmetry constant of a body with few vertices", Geometriae Dedicate, 90 (2002), 45--48. PDF, PS.

• E. D. Gluskin, A. E. Litvak, N. Tomczak-Jaegermann, "An example of the body without symmetric projections", Israel Journal of Math., 124 (2001), 267--277. PDF, PS.

• A. E. Litvak, "Kahane-Khinchin's inequality for the quasi-norms", Can. Math. Bull., 43 (2000), 368--379. PDF, PS.

• A. E. Litvak, N. Tomczak-Jaegermann, "Random aspects of high-dimensional convex bodies", GAFA, Lecture Notes in Math., 1745, 169--190, Springer-Verlag, 2000. PDF, PS.

• O. Guedon, A. E. Litvak, "Euclidean projections of p-convex body", GAFA, Lecture Notes in Math., 1745, 95--108, Springer-Verlag, 2000. PDF, PS.

• W. Banaszczyk, A. E. Litvak, A. Pajor, S. J. Szarek, "The flatness theorem for non-symmetric convex bodies via the local theory of Banach spaces", Math. of Oper. Research., 24 (1999), 728--750. PDF, PS.

• A. E. Litvak, V. D. Milman, A. Pajor, "Covering numbers and "low M*-estimate" for quasi-convex bodies", Proc. Amer. Math. Soc., 127 (1999), 1499--1507. PDF, PS.

• A. E. Litvak, "On the constant in the reverse Brunn-Minkowski inequality for p-convex balls", Convex Geometric Analysis, (Berkeley, CA, 1996), 129--137, Math. Sci. Res. Inst. Publ. V. 34, Cambridge Univ. Press, Cambridge, 1999. PDF, PS.

• A. E. Litvak, "The extension of the finite-dimensional version of Krivine's theorem to quasi-normed spaces", Convex Geometric Analysis, (Berkeley, CA, 1996), 139--148, Math. Sci. Res. Inst. Publ. V. 34, Cambridge Univ. Press, Cambridge, 1999. PDF, PS.

• A. E. Litvak, V. D. Milman, G. Schechtman, "Averages of norms and quasi-norms", Math. Ann., 312 (1998), 95--124. PDF, PS.

• A. E. Litvak, V. D. Milman, G. Schechtman, "Averages of norms and behaviour of families of projective caps on the sphere", C.R. Acad. Sci. Paris, Ser 1, Math., 325 (1997), 289--294. PDF, PS.

• A. E. Litvak, "Properties of the operator of discrete integrations and some applications", Vestnik St. Petersburg Univ., Math., 25 (1992), 28--30. PDF, PS.