Estimates of random vectors and processes

Research project of the National Science Center 2015/18/A/ST1/00553, run in the years 2016-2023

Short description of the project

Participants

• Rafał Latała - Principal Investigator
• Krzysztof Oleszkiewicz - Investigator
• Paweł Wolff - Investigator
• Marta Strzelecka - Investigator
• Witold Bednorz - Investigator

Former participants

• Dariusz Matlak - MSc student (October 2016 - September 2017)
• Maciej Bartczak - MSc student (November 2019-October 2020)
• Jacek Rutkowski - MSc student (November 2019-October 2020)
• Rafał Meller - PhD student (August 2016- October 2019)
• Bartłomiej Zawalski - PhD student (October 2019-September 2021)
• Piotr Nayar - Postdoc (October 2017 - September 2019)
• Witold Świątkowski - Postdoc (October 2019-September 2020)

Publications

Published

• Radosław Adamczak, Rafał Latała, Rafał Meller, Hanson-Wright inequality in Banach Spaces, Ann. Inst. Henri Poincaré Probab. Stat. 56 (2020), 2356-2376, doi:10.1214/19-AIHP1041, MR4164840. [arxiv version].
• Radosław Adamczak, Rafał Latała, Rafał Meller, Moments of Gaussian chaoses in Banach spaces, Electron. J. Probab. 26 (2021), no. 11, 1-36, doi:10.1214/20-EJP567, MR4216524. [arxiv version].
• Maciej Bartczak, Piotr Nayar, Szymon Zwara, Sharp variance-entropy comparison for nonnegative Gaussian quadratic forms IEEE Trans. Inform. Theory 67 (2021), no. 12, 7740-7751, doi:10.1109/TIT.2021.3113281, MR4346056. [arxiv version].
• Franck Barthe, Paweł Wolff, Positive Gaussian kernels also have Gaussian minimizers, Mem. Amer. Math. Soc. 276 (2022), no. 1359, v+90 pp., doi:, MR4384557. [arxiv version]
• Aline Bonami, Rafał Latała, Piotr Nayar, Tomasz Tkocz, Bounds on moments of weighted sums of finite Riesz products, J. Fourier Anal. Appl. 26 (2020), no. 6, 84, 31pp. doi:10.1007/s00041-020-09800-3, MR4175530. [arxiv version].
• Witold Bednorz, Rafał Martynek, On a contraction property of Bernoulli canonical processes, Bulletin Polish Acad. Sci. Math. 67 (2019), 187-209, doi:10.4064/ba8111-4-2019, MR4042785. [arxiv version]
• Tomasz Cieślak, Krzysztof Oleszkiewicz, Marcin Preisner, Marta Szumańska, Kinetic energy represented in terms of moments of vorticity and applications, J. Math. Fluid Mech. 21 (2019), Art. 53, 19 pp. doi:10.1007/s00021-019-0456-z, MR4010663. [arxiv version]
• Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz, Sharp comparison of moments and the log-concave moment problem, Adv. Math. 334 (2018), 389-416, doi:10.1016/j.aim.2018.06.014, MR3828740. [arxiv version]
• Rafał Latała, On Z_p-norms of random vectors, Zapiski Nauchnyh Seminarov POMI, 457 (2017), 211-225, reprinted in J. Math. Sci. (N.Y.) 238 (2019), 484-494 doi:10.1007/s10958-019-04252-7, MR3723583. [arxiv version]
• Rafał Latała, 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, MR3837281. [pdf]
• Rafał Latała, Piotr Nayar, Hadamard products and moments of random vectors, Adv. Math. 375 (2020), 107414, 10pp, doi:10.1016/j.aim.2020.107414, MR4170230. [arxiv version].
• Rafał Latała, Marta Strzelecka, Comparison of weak and strong moments for vectors with independent coordinates, Mathematika 64 (2018), 211-229, doi:10.1112/S0025579317000432, MR3778221. [arxiv version]
• Rafał Latała, Marta Strzelecka, Two-sided estimates for order statistics of log-concave random vectors, Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2017-2019 Volume II, 65-94, Lecture Notes in Math. 2266, Springer 2020, doi:10.1007/978-3-030-46762-3_3, MR4175758. [arxiv version].
• Rafał Latała, Witold Świątkowski, Norms of Randomized Circulant Matrices, Electron. J. Probab. 27 (2022), no. 80, 1-23, doi:10.1214/22-EJP799 MR4441144. [arxiv version]
• Rafał Latała, Ramon van Handel, Pierre Youssef, The dimension-free structure of nonhomogeneous random matrices, Invent. Math. 214 (2018), 1031-1080, doi:10.1007/s00222-018-0817-x, MR3878726. [arxiv version]
• Mokshay Madiman, Piotr Nayar, Tomasz Tkocz, Two remarks on generalized entropy power inequalities , Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2017-2019 Volume II, 169-185, Lecture Notes in Math. 2266, Springer 2020, doi:10.1007/978-3-030-46762-3_3, MR4175762. [arxiv version].
• Mokshay Madiman, Piotr Nayar, Tomasz Tkocz, Sharp moment-entropy inequalities and capacity bounds for symmetric log-concave distributions, IEEE Trans. Inform. Theory 67 (2021), 81-94. doi:10.1109/TIT.2020.3032371, MR4231940. [arxiv version].
• Rafał Meller, Two-sided moment estimates for a class of nonnegative chaoses, Statist. Probab. Lett. 119 (2016), 213-219, doi:10.1016/j.spl.2016.08.005, MR3555289, [arxiv version]
• Rafał Meller, Tail and moment estimates for a class of random chaoses of order two , Studia Math. 249 (2019), 1-32 doi:10.4064/sm170819-2-5, MR3984282, [arxiv version]

Accepted for publication

• Radosław Adamczak, Joscha Prochno, Marta Strzelecka, Michał Strzelecki Norms of structured random matrices, to appear in Math. Ann., doi:10.1007/s00208-023-02599-6. [arxiv version]
• Rafał Latała, Bounding suprema of canonical processes via convex hull, to appear in High Dimensional Probability IX. [arxiv version]
• Krzysztof Oleszkiewicz, Boolean functions with small second-order influences on the discrete cube, to appear in High Dimensional Probability IX. [arxiv version]

Preprints

• Bartłomiej Zawalski, On affine bodies with rotationally invariant sections. [arxiv version]
• Bartłomiej Zawalski, Differential characterization of quadratic surfaces. [arxiv version]