Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Probabilistic inequalities

2012/05/B/ST1/00412

Keywords:

concentration of measure isoperimetry hypercontraction martingales stochastic integrals random vectors stochastic processes random chaoses U-statistics logarithmically concave measures majorizing measure

Descriptors:

  • ST1_13:

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Uniwersytet Warszawski, Wydział Matematyki, Informatyki i Mechaniki

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Rafał Latała 

Number of co-investigators in the project: 9

Call: OPUS 3 - announced on 2012-03-15

Amount awarded: 616 720 PLN

Project start date (Y-m-d): 2013-02-06

Project end date (Y-m-d): 2016-02-05

Project duration:: 36 months (the same as in the proposal)

Project status: Project settled

Equipment purchased [PL]

  1. laptop (4 200 PLN)
  2. komputer stacjonarny z monitorem LCD (4 000 PLN)
  3. laptop (4 000 PLN)
  4. Laserowe urządzenie wielofunkcyjne (800 PLN)

Information in the final report

  • Publication in academic press/journals (60)
  • Book publications / chapters in book publications (4)
  1. Sudakov-type minoration for log-concave vectors
    Authors:
    Rafał Latała
    Academic press:
    Studia Mathematica (rok: 2014, tom: 223, strony: 251-274), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/sm223-3-5 - link to the publication
  2. Positivity improvement and Gaussian kernels
    Authors:
    Franck Barthe, Paweł Wolff
    Academic press:
    Comptes Rendus Mathématique. Académie des Sciences. Paris (rok: 2014, tom: 352, strony: 1017-1021), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.crma.2014.09.016 - link to the publication
  3. Moment estimates for chaoses generated by symmetric random variables with logarithmically convex tails
    Authors:
    Konrad Kolesko, Rafał Latała
    Academic press:
    Statistics and Probability Letters (rok: 2015, tom: 107, strony: 210-214), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2015.08.019 - link to the publication
  4. R -Boundedness versus γ -boundedness
    Authors:
    Stanisław Kwapień, Mark Veraar, Lutz Weis
    Academic press:
    Arkiv för Matematik (rok: 2016, tom: 54, strony: 125-145), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11512-015-0223-1 - link to the publication
  5. Two-sided bounds for L_p-norms of combinations of products of independent random variables
    Authors:
    Ewa Damek, Rafał Latała, Piotr Nayar, Tomasz Tkocz
    Academic press:
    Stochastic Processes and their Applications (rok: 2015, tom: 125, strony: 1688-1713), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2014.11.012 - link to the publication
  6. Kolmogorov's inequalities for martingales and the Haar system
    Authors:
    Adam Osękowski
    Academic press:
    Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie (rok: 2015, tom: 58, strony: 181-192), Wydawca: Societatea de Stiinte Matematice din România
    Status:
    Published
  7. A weak type inequality for submartingales and Itô processes
    Authors:
    Adam Osękowski
    Academic press:
    Bulletin of the Polish Academy of Sciences Mathematics (rok: 2015, tom: 63, strony: 73-88), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/ba63-1-9 - link to the publication
  8. Maximal inequalities for functions of bounded lower oscillation
    Authors:
    Adam Osękowski
    Academic press:
    Kyushu Journal of Mathematics (rok: 2014, tom: 68, strony: 297-306), Wydawca: Kyushu University
    Status:
    Published
    DOI:
    10.2206/kyushujm.68.297 - link to the publication
  9. R -Boundedness versus γ -boundedness
    Authors:
    Stanisław Kwapień, Mark Veraar, Lutz Weis
    Academic press:
    Arkiv för Matematik (rok: 2016, tom: 54, strony: 125-145), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11512-015-0223-1 - link to the publication
  10. On martingales whose exponential processes satisfy Muckenhoupt's condition A_1
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2013, tom: 83, strony: 1849-1853), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2013.04.012 - link to the publication
  11. A sharp maximal inequality for one-dimensional Dunkl martingales
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2015, tom: 105, strony: 114-119), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2015.06.008 - link to the publication
  12. Sharp Lp bound for holomorphic functions on the unit disc
    Authors:
    Adam Osękowski
    Academic press:
    Mediterranean Journal of Mathematics (rok: 2016, tom: 13, strony: 127-139), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00009-014-0495-x - link to the publication
  13. Sharp inequalities for BMO functions
    Authors:
    Adam Osękowski
    Academic press:
    Chinese Annals of Mathematics, Series B (rok: 2015, tom: 36, strony: 225-236), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11401-015-0887-7 - link to the publication
  14. L_1-norm of combinations of products of independent random variables
    Authors:
    Rafał Latała
    Academic press:
    Israel Journal of Mathematics (rok: 2014, tom: 203, strony: 295-308), Wydawca: Hebrew University
    Status:
    Published
    DOI:
    10.1007/s11856-014-1076-1 - link to the publication
  15. Moment inequality for the martingale square function
    Authors:
    Adam Osękowski
    Academic press:
    Bulletin of the Polish Academy of Sciences Mathematics (rok: 2013, tom: 61, strony: 169-180), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/ba61-2-11 - link to the publication
  16. A note on the Hanson-Wright inequality for random vectors with dependencies
    Authors:
    Radosław Adamczak
    Academic press:
    Electronic Communications in Probability (rok: 2015, tom: 20, strony: article 72,1-13), Wydawca: IMS
    Status:
    Published
    DOI:
    10.1214/ECP.v20-3829 - link to the publication
  17. On the boundedness of Bernoulli processes
    Authors:
    Witold Bednorz, Rafał Latała
    Academic press:
    Annals of Mathematics (rok: 2014, tom: 180, strony: 1167-1203), Wydawca: Princeton University
    Status:
    Published
    DOI:
    10.4007/annals.2014.180.3.8 - link to the publication
  18. Sharp Weak Type Inequality for Fractional Integral Operators Associated with d-Dimensional Walsh-Fourier Series
    Authors:
    Adam Osękowski
    Academic press:
    Integral Equations and Operator Theory (rok: 2014, tom: 78, strony: 589-600), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00020-013-2116-7 - link to the publication
  19. A prophet inequality for L^p-bounded dependent random variables
    Authors:
    Adam Osękowski
    Academic press:
    Positivity (rok: 2015, tom: 19, strony: 289-303), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11117-014-0295-3 - link to the publication
  20. Sharp Weak-Type Inequality for the Haar System, Harmonic Functions and Martingales
    Authors:
    Adam Osękowski
    Academic press:
    Bulletin of the Polish Academy of Sciences Mathematics (rok: 2014, tom: 62, strony: 187-196), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/ba62-2-7 - link to the publication
  21. A weak-type inequality for the martingale square function
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2014, tom: 95, strony: 139-143), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2014.08.019 - link to the publication
  22. Modified log-Sobolev inequalities for convex functions on the > real line. Sufficient conditions
    Authors:
    Radosław Adamczak, Michał Strzelecki
    Academic press:
    Studia Mathematica (rok: 2015, tom: 230, strony: 59-93), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/sm8319-12-2015 - link to the publication
  23. On the UMD constant of the space \ell_1^N
    Authors:
    Adam Osękowski
    Academic press:
    Colloquium Mathematicum (rok: 2016, tom: 142, strony: 135-147), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/cm142-1-7 - link to the publication
  24. Kolmogorov's inequalities for martingales and the Haar system
    Authors:
    Adam Osękowski
    Academic press:
    Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie (rok: 2015, tom: 58, strony: 181-192), Wydawca: Societatea de Stiinte Matematice din România
    Status:
    Published
    DOI:
    brak - link to the publication
  25. Sharp inequalities for martingales with values in \ell_\infty^N
    Authors:
    Adam Osękowski
    Academic press:
    Electronic Journal of Probability (rok: 2013, tom: 18, strony: article 73, 1-19), Wydawca: IMS
    Status:
    Published
    DOI:
    10.1214/EJP.v18-2667 - link to the publication
  26. Sharp L^{p,\infty} to L^q estimates for the dyadic-like maximal operators
    Authors:
    Adam Osękowski
    Academic press:
    Journal of Fourier Analysis and Applications (rok: 2014, tom: 20, strony: 911-933), Wydawca: Birhauser
    Status:
    Published
    DOI:
    10.1007/s00041-014-9338-1 - link to the publication
  27. On the UMD constant of the space \ell_1^N
    Authors:
    Adam Osękowski
    Academic press:
    Colloquium Mathematicum (rok: 2016, tom: 142, strony: 135-147), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/cm142-1-7 - link to the publication
  28. A note on suprema of canonical processes based on random variables with regular moments
    Authors:
    Rafał Latała, Tomasz Tkocz
    Academic press:
    Electronic Journal of Probability (rok: 2015, tom: Article 36, strony: 45674), Wydawca: IMS
    Status:
    Published
    DOI:
    10.1214/EJP.v20-3625 - link to the publication
  29. Weighted norm inequalities for fractional maximal operators - a Bellman function approach
    Authors:
    Rodrigo Banuelos, Adam Osękowski
    Academic press:
    Indiana University Mathematics Journal (rok: 2015, tom: 64, strony: 957-972), Wydawca: Indiana University
    Status:
    Published
    DOI:
    10.1512/iumj.2015.64.5534 - link to the publication
  30. On the suprema of Bernoulli processes
    Authors:
    Witold Bednorz, Rafał Latała
    Academic press:
    Comptes Rendus Mathématique. Académie des Sciences. Paris (rok: 2013, tom: 351, strony: 131-134), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.crma.2013.02.013 - link to the publication
  31. A note on suprema of canonical processes based on random variables with regular moments
    Authors:
    Rafał Latała, Tomasz Tkocz
    Academic press:
    Electronic Journal of Probability (rok: 2015, tom: Article 36, strony: 45674), Wydawca: IMS
    Status:
    Published
    DOI:
    10.1214/EJP.v20-3625 - link to the publication
  32. A new approach to Hardy-type inequalities
    Authors:
    Adam Osękowski
    Academic press:
    Archiv der Mathematik (rok: 2015, tom: 104, strony: 165-176), Wydawca: Birkhauser
    Status:
    Published
    DOI:
    10.1007/s00013-014-0722-5 - link to the publication
  33. On the suprema of Bernoulli processes
    Authors:
    Witold Bednorz, Rafał Latała
    Academic press:
    Comptes Rendus Mathématique. Académie des Sciences. Paris (rok: 2013, tom: 351, strony: 131-134), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.crma.2013.02.013 - link to the publication
  34. Sharp L^1(\ell^q) estimate for a sequence and its predictable projection
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2015, tom: 104, strony: 82-86), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2015.05.005 - link to the publication
  35. Sharp inequalities for martingales with values in \ell_\infty^N
    Authors:
    Adam Osękowski
    Academic press:
    Electronic Journal of Probability (rok: 2013, tom: 18, strony: article 73, 1-19), Wydawca: IMS
    Status:
    Published
    DOI:
    10.1214/EJP.v18-2667 - link to the publication
  36. Sharp inequalities for dyadic A_1 weights
    Authors:
    Adam Osękowski
    Academic press:
    Archiv der Mathematik (rok: 2013, tom: 101, strony: 181-190), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00013-013-0537-9 - link to the publication
  37. A prophet inequality for L^2-martingales
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2013, tom: 83, strony: 2319-2323), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2013.06.025 - link to the publication
  38. Maximal weak-type inequality for stochastic integrals
    Authors:
    Adam Osękowski
    Academic press:
    Electronic Communications in Probability (rok: 2014, tom: Article 25, strony: 45670), Wydawca: IMS
    Status:
    Published
    DOI:
    10.1214/ECP.v19-3151 - link to the publication
  39. Weak-L^oo inequalities for BMO functions
    Authors:
    Adam Osękowski
    Academic press:
    New York Journal of Mathematics (rok: 2015, tom: 21, strony: 699-713), Wydawca: The European Mathematical Information Service
    Status:
    Published
  40. Sharp L^{p,\infty} to L^q estimates for the dyadic-like maximal operators
    Authors:
    Adam Osękowski
    Academic press:
    Journal of Fourier Analysis and Applications (rok: 2014, tom: 20, strony: 911-933), Wydawca: Birhauser
    Status:
    Published
    DOI:
    10.1007/s00041-014-9338-1 - link to the publication
  41. Positivity improvement and Gaussian kernels
    Authors:
    Franck Barthe, Paweł Wolff
    Academic press:
    Comptes Rendus Mathématique. Académie des Sciences. Paris (rok: 2014, tom: 352, strony: 1017-1021), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.crma.2014.09.016 - link to the publication
  42. Sharp L^1(\ell^q) estimate for a sequence and its predictable projection
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2015, tom: 104, strony: 82-86), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2015.05.005 - link to the publication
  43. A logarithmic bound for a stopped Brownian motion
    Authors:
    Adam Osękowski
    Academic press:
    Stochastic Analysis and Applications (rok: 2016, tom: 34, strony: 65-74), Wydawca: Taylor and Francis
    Status:
    Published
    DOI:
    10.1080/07362994.2015.1099444 - link to the publication
  44. Sharp inequalities for geometric maximal operators associated with general measures
    Authors:
    Adam Osękowski
    Academic press:
    Analysis Mathematica (rok: 2013, tom: 39, strony: 287-296), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10476-013-0404-8 - link to the publication
  45. On martingales whose exponential processes satisfy Muckenhoupt's condition A_1
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2013, tom: 83, strony: 1849-1853), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2013.04.012 - link to the publication
  46. Modified log-Sobolev inequalities for convex functions on the > real line. Sufficient conditions
    Authors:
    Radosław Adamczak, Michał Strzelecki
    Academic press:
    Studia Mathematica (rok: 2015, tom: 230, strony: 59-93), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/sm8319-12-2015 - link to the publication
  47. A splitting procedure for Bellman functions and the action of dyadic maximal operators on L^p
    Authors:
    Adam Osękowski
    Academic press:
    Mathematika (rok: 2015, tom: 61, strony: 199-212), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1112/S0025579314000266 - link to the publication
  48. Sharp maximal estimates for BMO martingales
    Authors:
    Adam Osękowski
    Academic press:
    Osaka Journal of Mathematics (rok: 2015, tom: 52, strony: 1125-1143), Wydawca: Kinokuniya Company
    Status:
    Published
  49. Sharp L^2 log L inequalities for the Haar system and martingale transforms
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2014, tom: 94, strony: 91-97), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2014.07.006 - link to the publication
  50. A sharp maximal inequality for one-dimensional Dunkl martingales
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2015, tom: 105, strony: 114-119), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2015.06.008 - link to the publication
  51. A new approach to Hardy-type inequalities
    Authors:
    Adam Osękowski
    Academic press:
    Archiv der Mathematik (rok: 2015, tom: 104, strony: 165-176), Wydawca: Birkhauser
    Status:
    Published
    DOI:
    10.1007/s00013-014-0722-5 - link to the publication
  52. Sharp L^2 log L inequalities for the Haar system and martingale transforms
    Authors:
    Adam Osękowski
    Academic press:
    Statistics and Probability Letters (rok: 2014, tom: 94, strony: 91-97), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2014.07.006 - link to the publication
  53. Weak and strong moments of l_r-norms of log-concave vectors
    Authors:
    Rafał Latała, Marta Strzelecka
    Status:
    Accepted for publication
  54. Asymptotic entropic uncertainty relations
    Authors:
    Radosław Adamczak, Rafał Latała, Zbigniew Puchała, Karol Życzkowski
    Status:
    Accepted for publication
  55. Sharp LlogL estimates for Fourier multipliers
    Authors:
    Adam Osękowski
    Status:
    Accepted for publication
  56. A sharp weak-type (oo,oo) inequality for the Hilbert transform
    Authors:
    Adam Osękowski
    Status:
    Accepted for publication
  57. Sharp weak-type estimates for the dyadic-like maximal operators
    Authors:
    Adam Osękowski
    Status:
    Accepted for publication
  58. On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities
    Authors:
    Galyna Livshyts, Arnaud Marsiglietti, Piotr Nayar, Artem Zvavitch
    Status:
    Accepted for publication
  59. Sharp inequalities for the Haar system and martingale transforms
    Authors:
    Adam Osękowski
    Status:
    Accepted for publication
  60. Strong contraction and influences in tail spaces
    Authors:
    Steven Heilman, Elchanan Mossel i Krzysztof Oleszkiewicz
    Status:
    Accepted for publication
  1. Weak-type inequalities for maximal operators acting on Lorentz spaces
    Authors:
    Adam Osękowski
    Book:
    Calculus of Variations and PDEs, Banach Center Publications (rok: 2014, tom: 101, strony: 145-162), Wydawca: IMPAN
    Status:
    Published
  2. Modified Paouris inequality
    Authors:
    Rafał Latała
    Book:
    Geometric Aspects of Functional Analysis, Israel Seminar 2011-2013, seria Lecture Notes in Mathematics (rok: 2014, tom: 2116, strony: 293-307), Wydawca: Springer-Verlag
    Status:
    Published
  3. Modified Paouris inequality
    Authors:
    Rafał Latała
    Book:
    Geometric Aspects of Functional Analysis, Israel Seminar 2011-2013, seria Lecture Notes in Mathematics (rok: 2014, tom: 2116, strony: 293-307), Wydawca: Springer-Verlag
    Status:
    Published
  4. On mimicking Rademacher sums in tail spaces
    Authors:
    Krzysztof Oleszkiewicz
    Book:
    Status:
    Accepted for publication

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