Papers by Alexander Litvak

  1. 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, to appear. PDF, PS.
  2. 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., to appear, PDF, PS.
  3. Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "Uniform estimates for order statistics and Orlicz functions", Positivity, to appear, PDF, PS.
  4. 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, to appear (published online 4 August 2010, DOI: 10.1007/s00365-010-9117-4). PDF, PS.
  5. O. Guedon, A. E. Litvak, "On the symmetric average of a convex body", Advances in Geometry, to appear, PDF, PS.
  6. A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann, "Essentially-Euclidean convex bodies", Studia Math., 196 (2010), 207--221. PDF, PS.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. K. Bezdek, A. E. Litvak, "On the vertex index of convex bodies", Adv. Math., 215 (2007), 626--641. PDF, PS.
  13. 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.
  14. 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.
  15. A. E. Litvak, V. D. Milman, A. Pajor, N. Tomczak-Jaegermann, "Entropy extension", Funct. Anal. Appl., 40 (2006), 298--303. PDF, PS.
  16. Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "On the minimum of several random variables", Proc. AMS, 134 (2006), 3665--3675. PDF, PS.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. A. E. Litvak, "On the dual form of "Low M* -estimate" in the quasi-convex case", Positivity, 8 (2004), 401--406. PDF, PS.
  22. 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.
  23. Y. Gordon, A. E. Litvak, M. Meyer, A. Pajor, "Jonn's decomposition in the general case and applications", J. of Diff. Geometry, 68 (2004), 99--119. PDF, PS.
  24. 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.
  25. 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.
  26. A. E. Litvak, V. D. Milman, "Euclidean sections of direct sums of normed spaces", Can. Math. Bull., 46 (2003), 242--251. PDF, PS.
  27. 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.
  28. Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "Orlicz Norms of Sequences of Random Variables", Ann. Probab., 30 (2002), 1833--1853. PDF, PS.
  29. 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.
  30. 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.
  31. E. D. Gluskin, A. E. Litvak, "On the asymmetry constant of a body with few vertices", Geometriae Dedicate, 90 (2002), 45--48. PDF, PS.
  32. 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.
  33. A. E. Litvak, "Kahane-Khinchin's inequality for the quasi-norms", Can. Math. Bull., 43 (2000), 368--379. PDF, PS.
  34. 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.
  35. O. Guedon, A. E. Litvak, "Euclidean projections of p-convex body", GAFA, Lecture Notes in Math., 1745, 95--108, Springer-Verlag, 2000. PDF, PS.
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. A. E. Litvak, V. D. Milman, G. Schechtman, "Averages of norms and quasi-norms", Math. Ann., 312 (1998), 95--124. PDF, PS.
  41. 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.
  42. A. E. Litvak, "Properties of the operator of discrete integrations and some applications", Vestnik St. Petersburg Univ., Math., 25 (1992), 28--30. PDF, PS.