All papers

  1. A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef, "Circular law for sparse random regular digraphs," submitted. PDF.
  2. A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef, "Structure of eigenvectors of random regular digraphs," submitted. PDF.
  3. A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef, "The smallest singular value of a shifted $d$-regular random square matrix," Prob. Th. Rel. Fields, to appear. PDF.
  4. A. E. Litvak, K. Tikhomirov, "Order statistics of vectors with dependent coordinates, and the Karhunen--Loeve basis," Annals of Applied Prob., 28 (2018), 2083--2104. PDF.
  5. A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef, "The rank of random regular digraphs of constant degree," J. of Complexity, 48 (2018), 103--110. PDF.
  6. A. E. Litvak, "Around the simplex mean width conjecture," Analytic Aspects of Convexity, Springer INdAM Series, 25 (2018), 73--84. PDF, PS.
  7. A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef, "Adjacency matrices of random digraphs: singularity and anti-concentration," J. of Math. Analysis and Appl., 445 (2017), 1447--1491. Winner of 2017 JMAA Ames Award . PDF, PS.
  8. A. E. Litvak, K. Tikhomirov, "Estimates for order statistics in terms of quantiles," Zapiski Nauchnykh Seminarov POMI, 457 (2017), 265--275; English translation: Journal of Math. Sciences, to appear. PDF, PS.
  9. O. Guedon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "On the interval of fluctuation of the singular values of random matrices," Journal of the European Mathematical Society, 19 (2017), 1469--1505. PDF, PS.
  10. O. Guedon, A. Hinrichs, A. E. Litvak, J. Prochno, "On the expectation of operator norms of random matrices," GAFA, Lecture Notes in Math., 2169 (2017), 151--162. PDF.
  11. K. Bezdek, A. E. Litvak, "Packing convex bodies by cylinders," Discrete and Computational Geometry, 55 (2016), 725--738. PDF, PS.
  12. D. Alonso-Gutierrez, A. E. Litvak, N. Tomczak-Jaegermann, "On the isotropic constant of random polytopes," Journal of Geometric Analysis, 26 (2016), 645--662. PDF, PS.
  13. A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef, "Anti-concentration property for random digraphs and invertibility of their adjacency matrices," C.R. Math. Acad. Sci. Paris, 354 (2016), 121--124. PDF, PS, Offprint
  14. Z. Kabluchko, A. E. Litvak, D. Zaporozhets, "On the expected maximum of correlated Gaussian variables," Zapiski Nauchnykh Seminarov POMI, 442 (2015), 75--96; English translation: Journal of Math. Sciences, 225 (2017), 770--787. PDF.
  15. A. E. Litvak, M. Rudelson, N. Tomczak-Jaegermann, "On approximation by projections of polytopes with few facets," Israel Journal of Math., 203 (2014), 141--160. PDF, PS.
  16. A. E. Litvak, S. Spektor, "Quantitative version of a Silverstein's result," GAFA, Lecture Notes in Math., 2116 (2014), 335--340. PDF, PS.
  17. B. Collins, P. Gawron, A. E. Litvak, K. Zyczkowski, "Numerical range for random matrices," J. of Math. Analysis and Appl., 418 (2014), 516--533. PDF
  18. O. Guedon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Restricted isometry property for random matrices with heavy tailed columns," C.R. Math. Acad. Sci. Paris, 352 (2014), 431--434. PDF, PS.
  19. R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Tail estimates for norms of sums of log-concave random vectors," Proc. London Math. Soc., 108 (2014), 600--637. PDF, PS.
  20. R. Adamczak, R. Latala, A. E. Litvak, K. Oleszkiewicz, A. Pajor, N. Tomczak-Jaegermann, "A short proof of Paouris' inequality," Canadian Math. Bull, 57 (2014), 3--8. PDF, PS.
  21. R. Adamczak, O. Guedon, R. Latala, A. E. Litvak, K. Oleszkiewicz, A. Pajor, N. Tomczak-Jaegermann, "Moment estimates for convex measures," Electron. J. Probab., 17 no. 101 (2012), 1--19. PDF, PS.
  22. A. E. Litvak, O. Rivasplata, "Smallest singular value of sparse random matrices," Stud. Math., 212 (2012), 195--218. PDF, PS.
  23. R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann, "Chevet type inequality and norms of submatrices," Studia Math., 210 (2012), 35--56. PDF, PS.
  24. E. D. Gluskin, A. E. Litvak, "A remark on vertex index of the convex bodies," GAFA, Lecture Notes in Math., 2050, 255--265, Springer, Berlin, 2012. PDF, PS.
  25. Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "Uniform estimates for order statistics and Orlicz functions," Positivity, 16 (2012), 1--28. PDF, PS.
  26. 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.
  27. O. Guedon, A. E. Litvak, "On the symmetric average of a convex body," Advances in Geometry, 11 (2011), 615--622. PDF, PS.
  28. 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.
  29. 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.
  30. 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.
  31. A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann, "Essentially-Euclidean convex bodies," Studia Math., 196 (2010), 207--221. PDF, PS.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. K. Bezdek, A. E. Litvak, "On the vertex index of convex bodies," Adv. Math., 215 (2007), 626--641. PDF, PS.
  38. 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.
  39. 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.
  40. A. E. Litvak, V. D. Milman, A. Pajor, N. Tomczak-Jaegermann, "Entropy extension," Funct. Anal. Appl., 40 (2006), 298--303. PDF, PS.
  41. Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "On the minimum of several random variables," Proc. AMS, 134 (2006), 3665--3675. PDF, PS.
  42. 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.
  43. 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.
  44. 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.
  45. 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.
  46. A. E. Litvak, "On the dual form of "Low M* -estimate" in the quasi-convex case," Positivity, 8 (2004), 401--406. PDF, PS.
  47. 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.
  48. 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.
  49. 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.
  50. 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.
  51. A. E. Litvak, V. D. Milman, "Euclidean sections of direct sums of normed spaces," Can. Math. Bull., 46 (2003), 242--251. PDF, PS.
  52. 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.
  53. Y. Gordon, A. E. Litvak, C. Schuett, E. Werner, "Orlicz Norms of Sequences of Random Variables," Ann. Probab., 30 (2002), 1833--1853. PDF, PS.
  54. 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.
  55. 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.
  56. E. D. Gluskin, A. E. Litvak, "On the asymmetry constant of a body with few vertices," Geometriae Dedicate, 90 (2002), 45--48. PDF, PS.
  57. 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.
  58. A. E. Litvak, "Kahane-Khinchin's inequality for the quasi-norms," Can. Math. Bull., 43 (2000), 368--379. PDF, PS.
  59. 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.
  60. O. Guedon, A. E. Litvak, "Euclidean projections of p-convex body," GAFA, Lecture Notes in Math., 1745, 95--108, Springer-Verlag, 2000. PDF, PS.
  61. 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.
  62. 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.
  63. 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.
  64. 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.
  65. A. E. Litvak, V. D. Milman, G. Schechtman, "Averages of norms and quasi-norms," Math. Ann., 312 (1998), 95--124. PDF, PS.
  66. 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.
  67. A. E. Litvak, "Properties of the operator of discrete integrations and some applications," Vestnik St. Petersburg Univ., Math., 25 (1992), 28--30. PDF, PS.