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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Estimates of random vectors and processes

2015/18/A/ST1/00553

Keywords:

random vector stochastic process concentration of measure random chaos logarithmically concave measure chaining method

Descriptors:

  • ST1_13:
  • ST1_8:

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: 12

Call: MAESTRO 7 - announced on 2015-06-15

Amount awarded: 1 513 800 PLN

Project start date (Y-m-d): 2016-04-12

Project end date (Y-m-d): 2023-04-11

Project duration:: 84 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. Oprogramowanie Mathematica (7 000 PLN)
  2. laptop (5 000 PLN)
  3. laptop (10 000 PLN)

Information in the final report

  • Publication in academic press/journals (20)
  • Book publications / chapters in book publications (5)
  1. Two-sided moment estimates for a class of nonnegative chaoses
    Authors:
    Rafał Meller
    Academic press:
    Statistics & Probability Letters (rok: 2016, tom: 119, strony: 213-219), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spl.2016.08.005 - link to the publication
  2. Sharp comparison of moments and the log-concave moment problem
    Authors:
    Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
    Academic press:
    Advances in Mathematics (rok: 2018, tom: 334, strony: 389-416), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2018.06.014 - link to the publication
  3. On Z_p-norms of random vectors
    Authors:
    Rafał Latała
    Academic press:
    Zapiski Nauchnyh Seminarov POMI (rok: 2017, tom: 457, strony: 211-225), Wydawca: Steklov Mathematical Institute, St Petersburg, Rosja
    Status:
    Published
  4. Sharp moment-entropy inequalities and capacity bounds for symmetric log-concave distributions
    Authors:
    Mokshay Madiman, Piotr Nayar, Tomasz Tkocz
    Academic press:
    Institute of Electrical and Electronics Engineers. Transactions on Information Theory (rok: 2021, tom: 67, strony: 81-94), Wydawca: Institute of Electrical and Electronics Engineers
    Status:
    Published
    DOI:
    10.1109/TIT.2020.3032371 - link to the publication
  5. Sharp variance-entropy comparison for nonnegative Gaussian quadratic forms
    Authors:
    Maciej Bartczak, Piotr Nayar, Szymon Zwara
    Academic press:
    Institute of Electrical and Electronics Engineers. Transactions on Information Theory (rok: 2021, tom: 67, strony: 7740–7751), Wydawca: Institute of Electrical and Electronics Engineers
    Status:
    Published
    DOI:
    10.1109/TIT.2021.3113281 - link to the publication
  6. Positive Gaussian kernels also have Gaussian minimizers
    Authors:
    Franck Barthe, Paweł Wolff
    Academic press:
    Memoirs of the American Mathematical Society (rok: 2022, tom: 276, strony: v+90), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/memo/1359 - link to the publication
  7. Tail and moment estimates for a class of random chaoses of order two
    Authors:
    Rafał Meller
    Academic press:
    Studia Mathematica (rok: 2019, tom: 249, strony: 11689), Wydawca: Instytut Matematyczny PAN
    Status:
    Published
    DOI:
    10.4064/sm170819-2-5 - link to the publication
  8. Moments of Gaussian chaoses in Banach spaces
    Authors:
    Radosław Adamczak, Rafał Latała, Rafał Meller
    Academic press:
    Electronic Journal of Probability (rok: 2021, tom: 26, strony: Art. no 11, 1-36), Wydawca: Institute of Mathematical Statistics and Bernoulli Society
    Status:
    Published
    DOI:
    10.1214/20-EJP567 - link to the publication
  9. Hadamard products and moments of random vectors
    Authors:
    Rafał Latała, Piotr Nayar
    Academic press:
    Advances in Mathematics (rok: 2020, tom: 375, strony: 10pp), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2020.107414 - link to the publication
  10. Hanson-Wright inequality in Banach Spaces
    Authors:
    Radosław Adamczak, Rafał Latała, Rafał Meller
    Academic press:
    Annales de l'Institut Henri Poincaré Probabilités et Statistiques (rok: 2020, tom: 56, strony: 2356-2376), Wydawca: Inst. Henri Poincaré
    Status:
    Published
    DOI:
    10.1214/19-AIHP1041 - link to the publication
  11. Sharp variance-entropy comparison for nonnegative Gaussian quadratic forms
    Authors:
    Maciej Bartczak, Piotr Nayar, Szymon Zwara
    Academic press:
    Institute of Electrical and Electronics Engineers. Transactions on Information Theory (rok: 2021, tom: 67, strony: 7740–7751), Wydawca: Institute of Electrical and Electronics Engineers
    Status:
    Published
    DOI:
    10.1109/TIT.2021.3113281 - link to the publication
  12. On a contraction property of Bernoulli canonical processes
    Authors:
    Witold Bednorz, Rafał Martynek
    Academic press:
    Bulletin of the Polish Academy of Sciences. Mathematics (rok: 2019, tom: 67, strony: 187-209), Wydawca: Instytut Matematyczny PAN
    Status:
    Published
    DOI:
    10.4064/ba8111-4-2019 - link to the publication
  13. The dimension-free structure of nonhomogeneous random matrices
    Authors:
    Rafał Latała, Ramon van Handel, Pierre Youssef
    Academic press:
    Inventiones mathematicae (rok: 2018, tom: 214, strony: 1031-1080), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00222-018-0817-x - link to the publication
  14. Comparison of weak and strong moments for vectors with independent coordinates
    Authors:
    Rafał Latała, Marta Strzelecka
    Academic press:
    Mathematika (rok: 2018, tom: 64, strony: 211-229), Wydawca: University College London
    Status:
    Published
    DOI:
    10.1112/S0025579317000432 - link to the publication
  15. Kinetic energy represented in terms of moments of vorticity and applications
    Authors:
    Tomasz Cieślak, Krzysztof Oleszkiewicz, Marcin Preisner, Marta Szumańska
    Academic press:
    Journal of Mathematical Fluid Mechanics (rok: 2019, tom: 21, strony: Art. 53, 19 pp.), Wydawca: Birkhäuser Verlag
    Status:
    Published
    DOI:
    10.1007/s00021-019-0456-z - link to the publication
  16. Norms of randomized circulant matrices
    Authors:
    Rafał Latała, Witold Świątkowski
    Academic press:
    Electronic Journal of Probability (rok: 2022, tom: 27, strony: Art. no 80, 1-23), Wydawca: Institute of Mathematical Statistics and Bernoulli Society
    Status:
    Published
    DOI:
    10.1214/22-ejp799 - link to the publication
  17. Sharp comparison of moments and the log-concave moment problem
    Authors:
    Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
    Academic press:
    Advances in Mathematics (rok: 2018, tom: 334, strony: 389-416), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2018.06.014 - link to the publication
  18. Bounds on moments of weighted sums of finite Riesz products
    Authors:
    Aline Bonami, Rafał Latała, Piotr Nayar, Tomasz Tkocz
    Academic press:
    Journal of Fourier Analysis and Applications (rok: 2020, tom: 26, strony: Art.84, 31pp), Wydawca: Birkhauser
    Status:
    Published
    DOI:
    10.1007/s00041-020-09800-3 - link to the publication
  19. Hanson-Wright inequality in Banach Spaces
    Authors:
    Radosław Adamczak, Rafał Latała, Rafał Meller
    Academic press:
    Annales de l'Institut Henri Poincaré Probabilités et Statistiques (rok: 2020, tom: 56, strony: 2356-2376), Wydawca: Inst. Henri Poincaré
    Status:
    Published
    DOI:
    10.1214/19-AIHP1041 - link to the publication
  20. Norms of structured random matrices
    Authors:
    Radosław Adamczak, Joscha Prochno, Marta Strzelecka, Michał Strzelecki
    Status:
    Accepted for publication
  1. On some problems concerning log-concave random vectors
    Authors:
    Rafał Latała
    Book:
    Convexity and Concentration (rok: 2017, tom: 161, strony: 525-539), Wydawca: Springer
    Status:
    Published
  2. Two-sided estimates for order statistics of log-concave random vectors
    Authors:
    Rafał Latała, Marta Strzelecka
    Book:
    Geometric Aspects of Functional Analysis (rok: 2020, tom: 2266, strony: 65-94), Wydawca: Springer
    Status:
    Published
  3. Two Remarks on Generalized Entropy Power Inequalities
    Authors:
    Mokshay Madiman, Piotr Nayar, Tomasz Tkocz
    Book:
    Geometric Aspects of Functional Analysis (rok: 2020, tom: 2266, strony: 169-185), Wydawca: Springer
    Status:
    Published
  4. Boolean Functions with Small Second-Order Influences on the Discrete Cube
    Authors:
    Krzysztof Oleszkiewicz
    Book:
    Status:
    Accepted for publication
  5. Bounding suprema of canonical processes via convex hull
    Authors:
    Rafał Latała
    Book:
    Status:
    Accepted for publication

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