Papers by Rafal Latala

Polska wersja tej strony

Preprints

  1. On Z_p-norms of random vectors [pdf].

To appear

  1. with M. Strzelecka, Comparison of weak and strong moments for vectors with independent coordinates [pdf], to appear in Mathematika.

Published

Pdf files below may slightly differ from the published versions.
  1. On some problems concerning log-concave random vectors, Convexity and Concentration, 525-539, The IMA Volumes in Mathematics and its Applications 161, Springer 2017, doi:10.1007/978-1-4939-7005-6_16. [pdf]
  2. with D. Matlak, Royen's proof of the Gaussian correlation inequality, Geometric Aspects of Functional Analysis, Israel Seminar (GAFA) 2014-2016, 265-275, Lecture Notes in Math. 2169, Springer 2017, doi:10.1007/978-3-319-45282-1_17. [pdf]
  3. with M. Strzelecka, Weak and strong moments of l_r-norms of log-concave vectors, Proc. Amer. Math. Soc. 144 (2016), 3597-3608, doi:10.1090/proc/13003, MR3503729. [pdf]
  4. with R. Adamczak, Z. Puchala i K. Zyczkowski, Asymptotic entropic uncertainty relations, J. Math. Phys. 57 (2016), 032204, 24 pp. doi:10.1063/1.4944425, MR3478525. [pdf]
  5. with K. Kolesko, Moment estimates for chaoses generated by symmetric random variables with logarithmically convex tails, Statist. Probab. Lett. 107 (2015), 210-214, doi:10.1016/j.spl.2015.08.019, MR3412778. [pdf]
  6. with T. Tkocz, A note on suprema of canonical processes based on random variables with regular moments, Electron. J. Probab. 20 (2015), no. 36, 1-17, doi:10.1214/EJP.v20-3625, MR3335827. [pdf]
  7. with E. Damek, P. Nayar and T. Tkocz Two-sided bounds for L_p-norms of combinations of products of independent random variables, Stochastic Process. Appl. 125 (2015), 1688-1713, doi:10.1016/j.spa.2014.11.012, MR3310361. [pdf]
  8. with W. Bednorz, On the boundedness of Bernoulli processes, Ann.of Math. (2) 180 (2014), 1167-1203, doi:10.4007/annals.2014.180.3.8, MR3245015. [pdf]
  9. Sudakov-type minoration for log-concave vectors, Studia Math. 223 (2014), 251-274, doi:10.4064/sm223-3-5, MR3274967. [pdf]
  10. L_1-norm of combinations of products of independent random variables, Israel J. Math. 203 (2014), 295-308 doi:10.1007/s11856-014-1076-1, MR3273442. [pdf ]
  11. Modified Paouris inequality, in: Geometric Aspects of Functional Analysis, Israel Seminar 2011-2013, 293-307, Lecture Notes in Math. 2116, Springer 2014, doi:10.1007/978-3-319-09477-9_19, MR3364693. [pdf]
  12. with R. Adamczak, A. Litvak, A. Pajor and N. Tomczak-Jaegermann, Tail estimates for norms of sums of log-concave random vectors, Proc. London Math. Soc. 108 (2014), 600-637, doi:10.1112/plms/pdt031, MR3180591. [pdf]
  13. with R. Adamczak, A. Litvak, K. Oleszkiewicz, A. Pajor and N. Tomczak-Jaegermann, A short proof of Paouris' inequality, Can. Math. Bull. 57 (2014), 3-8, doi:10.4153/CMB-2012-014-5, MR3150710. [pdf]
  14. Maximal inequalities for centered norms of sums of independent random vectors, in: High Dimensional Probability VI, The Banff Volume, Progr. Probab. 66, 63-71, Birkhauser 2013, doi:10.1007/978-3-0348-0490-5_4. [pdf]
  15. with W. Bednorz, On the suprema of Bernoulli processes, C. R. Math. Acad. Sci. Paris 351 (2013), 131-134, doi:10.1016/j.crma.2013.02.013, MR3038002. [pdf]
  16. with R. Adamczak, O. Guédon, A. Litvak, K. Oleszkiewicz, A. Pajor and N. Tomczak-Jaegermann, Moment estimates for convex measures, Electron. J. Probab. 17 (2012),no. 101, 1-19, doi:10.1214/EJP.v17-2150, MR3005719. [pdf]
  17. with R. Adamczak, Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails, Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012), 1103-1136, doi:10.1214/11-AIHP441, MR3052405. [pdf]
  18. with R. Adamczak, A. Litvak, A. Pajor and N. Tomczak-Jaegermann, Chevet type inequality and norms of submatrices, Studia Math. 210 (2012), 35-56, doi:10.4064/sm210-1-3, MR2949869. [pdf]
  19. Moments of unconditional logarithmically concave vectors, in: Geometric Aspects of Functional Analysis, Israel Seminar 2006-2010, 301-315, Lecture Notes in Math. 2050, Springer 2012, doi:10.1007/978-3-642-29849-3_17, MR2985299. [pdf]
  20. Weak and strong moments of random vectors, Marcinkiewicz Centenary Volume, Banach Center Publ. 95 (2011), 115-121, doi:10.4064/bc95-0-8, MR2918093. [pdf]
  21. with R. Adamczak, A. Litvak, A. Pajor and N. Tomczak-Jaegermann, Geometry of log-concave Ensembles of random matrices and approximate reconstruction, C. R. Math. Acad. Sci. Paris. 349 (2011), 783-786, doi:10.1016/j.crma.2011.06.025, MR2825941. [pdf]
  22. Order statistics and concentration of l_r norms for log-concave vectors, J. Funct. Anal. 261 (2011), 681-696, doi:10.1016/j.jfa.2011.02.013, MR2799576. [pdf]
  23. Gaussian approximation of moments of sums of independent symmetric random variables with logarithmically concave tails, IMS Collections 5 (2009), High Dimensional Probability V: The Luminy Volume, 37-42, doi:10.1214/09-IMSCOLL503, MR2797938. [pdf]
  24. On weak tail domination of random vectors, Bull. Polish Acad. Sci. Math. 57 (2009), 75-80, doi:10.4064/ba57-1-8, MR2520452. [pdf]
  25. with J.O. Wojtaszczyk, On the infimum convolution inequality, Studia Math. 189 (2008), 147-187, doi:10.4064/sm189-2-5, MR2449135. [pdf]
  26. with R. Adamczak, The LIL for U-statistics in Hilbert spaces , J. Theoret. Probab. 21 (2008), 704-744, doi:10.1007/s10959-007-0134-6, MR2425366. [pdf]
  27. with R. Adamczak, The LIL for canonical U-statistics, Ann. Probab. 36 (2008), 1023-1058, doi:10.1214/07-AOP351, MR2408582. [pdf]
  28. On the boundedness of Bernoulli processes over thin sets, Elect. Comm. in Probab. 13 (2008), 175-186, doi:10.1214/ECP.v13-1362, MR2399279. [pdf]
  29. with W. Bednorz and K. Latuszynski, A regeneration proof of the Central Limit Theorem for uniformly ergodic Markov chains, Elect. Comm. in Probab. 13 (2008), 85-98, doi:10.1214/ECP.v13-1354, MR2386065. [pdf]
  30. with P. Mankiewicz, K. Oleszkiewicz and N. Tomczak-Jaegermann, Banach-Mazur distances and projections on random subgaussian polytopes, Discrete Comput. Geom. 38 (2007), 29-50, doi:10.1007/s00454-007-1326-7, MR2322114. [pdf]
  31. Estimates of moments and tails of Gaussian chaoses, Ann. Probab. 34 (2006), 2315-2331, doi:10.1214/009117906000000421, MR2294983. [pdf]
  32. with K. Oleszkiewicz, Small ball probability estimates in terms of width, Studia Math. 169 (2005), 305-314, doi:10.4064/sm169-3-6, MR2140804. [pdf]
  33. Some estimates of norms of random matrices, Proc. Amer. Math. Soc. 133 (2005), 1273-1282, doi:10.1090/S0002-9939-04-07800-1, MR2111932. [pdf]
  34. Miedzy Poincarém a Sobolewem, Wiadomosci Matematyczne 40 (2004), 67-76 (in Polish), MR2337174. [pdf]
  35. with R. Lochowski, Moment and tail estimates for multidimensional chaoses generated by positive random variables with logarithmically concave tails, Progr. Probab. 56 (2003), 77-92, doi:10.1007/978-3-0348-8069-5_7, MR2073428. [pdf]
  36. with S. Kwapien, K. Oleszkiewicz and J. Zinn, On the limit set in the law of the iterated logarithm for $U$-statistics of order two, Progr. Probab. 55 (2003), 111-126, doi:10.1007/978-3-0348-8059-6_7, MR2033884. [pdf]
  37. On some inequalities for Gaussian measures, in: Proceedings of the International Congress of Mathematicians, vol II, 813-822, Higher Education Press, Beijing 2002, MR1957087. [pdf]
  38. with R. Bañuelos and P. Mendez-Hernandez, A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes, Proc. Amer. Math. Soc. 29 (2001), 2997-3008, doi:10.1090/S0002-9939-01-06137-8, MR1840105. [pdf]
  39. with E. Giné, S. Kwapien and J. Zinn, The LIL for canonical U-statistics of order 2, Ann. Probab. 29 (2001), 520-557, doi:10.1214/aop/1008956343, MR1825163. [pdf]
  40. with J. Zinn, Necessary and Sufficient Conditions for the Strong Law of Large Numbers for U-statistics, Ann. Probab. 28 (2000), 1908-1924, doi:10.1214/aop/1019160513, MR1813848. [pdf]
  41. with K. Oleszkiewicz, Between Sobolev and Poincare , in: Geometric Aspects of Functional Analysis, Israel Seminar (GAFA) 1996-2000, 147-168, Lecture Notes in Math. 1745, Springer Verlag, Berlin 2000, doi:10.1007/BFb0107213, MR1796718. [pdf]
  42. with E. Giné and J. Zinn, Exponential and moment inequalities for U-statistics, in: High Dimensional Probability II, 13-38, Progr. Probab. 47, Birkhauser, Boston 2000, doi:10.1007/978-1-4612-1358-1_2, MR1857312. [pdf]
  43. with K. Oleszkiewicz, Gaussian measures of dilatations of convex symmetric sets , Ann. Probab. 27 (1999), 1922-1938, doi:10.1214/aop/1022874821, MR1742894. [pdf]
  44. A note on the maximal inequalities for VC-classes , in: Advances in stochastic inequalities (Atlanta, GA, 1997), 125-134, Contemp. Math. 234, Amer. Math. Soc., Providence 1999, doi:10.1090/conm/234/03450, MR1694768. [pdf]
  45. Tail and moment estimates for some types of chaos , Studia Math. 135 (1999), 39-53, MR1686370. [pdf]
  46. On the equivalence between geometric and arithmetic means for log-concave measures , in: Convex geometric analysis (Berkeley, CA, 1996), 123-127, Math. Sci. Res. Inst. Publ. 34, Cambridge Univ. Press, Cambridge 1999, MR1665584. [pdf]
  47. On the almost sure boundedness of norms of some empirical operators, Statist. Probab. Lett. 38 (1998), 177-182, doi:10.1016/S0167-7152(98)00002-9, MR1627869. [pdf]
  48. Sudakov minoration principle and supremum of some processes , Geom. Funct. Anal. 7 (1997), 936-953, doi:10.1007/s000390050031, MR1475551. [pdf]
  49. Estimation of moments of sums of independent real random variables, Ann. Probab. 25 (1997), 1502-1513, doi:10.1214/aop/1024404522, MR1457628. [pdf]
  50. with M. Pycia, On the volume of convex hulls of sets on spheres, Geom. Dedicata 63 (1996), 153-157, doi:10.1007/BF00148215, MR1413627.
  51. Tail and moment estimates for sums of independent random vectors with logarithmically concave tails, Studia Math. 118 (1996), 301-304, MR1388035. [pdf]
  52. A note on the Ehrhard inequality , Studia Math. 118 (1996), 169-174, MR1389763. [pdf]
  53. with S. Kwapien and K. Oleszkiewicz, Comparison of moments of sums of independent random variables and differential inequalities, J. Funct. Anal. 136 (1996), 258-268, doi:10.1006/jfan.1996.0030, MR1375162.
  54. with K. Oleszkiewicz, A note on sums of independent uniformly distributed random variables, Colloq. Math. 68 (1995), 197-206, MR1321042. [pdf]
  55. with K. Oleszkiewicz, On the best constant in the Khinchin-Kahane inequality, Studia Math. 109 (1994), 101-104, MR1267715. [pdf]

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