
AffiliationProbability Theory Group, Institute of Mathematics, University of Warsaw Scientific interests High Dimensional Probability Selected current activitiesPrincipal investigator in the project The concentration of measure phenomenon of the National Science Center. Associate editor for Bernoulli Coorganizer of a monthly Faculty Colloquium 

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Institute of Mathematics, University of Warsaw / ul. Banacha 2 / 02097 Warszawa / POLAND
r "dot" surname "at" mimuw "dot" edu "dot" pl (work)
radek "dot" "surname" "at" o2 "dot" pl (private)
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RP II  semestr zimowy 2018/2019
Seminarium magisterskie z rachunku prawdopodobieństwa
Elementy teorii macierzy losowych  notatki
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Scientific interests  a brief descriptionMy research field is probability theory, with focus on high dimensional phenomena. I am particularly interested in concentration inequalities and their applications. Other areas I have been working on are Random Matrix Theory, Markov chains, quantum information, the theory of $U$statistics and branching particle systems. Coauthors

The main links below lead to journal versions of the articles. The arXiv versions may differ (in fact do differ) from the final ones. You may also visit my MathSciNet , Google Scholar or ORCID profiles.
1. Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses, Bulletin Polish Acad. Sci. Math. 53 (2005), 221238. arXiv version
2. Moment Inequalities for Ustatistics, Ann. Probab. 2006, Vol. 34, No. 6, 22882314. arXiv version
3. With R. Latała, The LIL for canonical Ustatistics, Ann. Probab. 2008, Vol. 36, No. 3, 10231058. arXiv version
4. With R. Latała, The LIL for Ustatistics in Hilbert spaces, J. Theoret. Probab. 21 (2008), 704744. arXiv version
5. A tail inequality for suprema of unbounded empirical processes with applications to Markov chains, Electronic Journal of Probability, Vol. 13 (2008), 10001034.
6. A few remarks on the operator norm of random Toeplitz matrices, J. Theoret. Probab, Volume 23 (2010), Number 1, 85108. arXiv version
7. With O. Guédon, A. Litvak, A. Pajor and N. TomczakJaegermann, Smallest singular value of random matrices with independent columns, Comptes Rendus Mathematique Vol. 346, Issues 1516, 2008, 853856
8. With A. Litvak, A. Pajor and N. TomczakJaegermann, Quantitative estimates of the convergence of the empirical covariance matrix in Logconcave Ensembles. J. Amer. Math. Soc. 23 (2010), 535561. arXiv version
9. With A. Litvak, A. Pajor and N. TomczakJaegermann, Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling. Constructive Approximation Vol. 34, No. 1, 6188. arXiv version
10. With R. Latała, Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails. Annales de l’Institut Henri Poincaré. Probab. Statist. Volume 48, Number 4 (2012), 11031136. arXiv version
11. With O. Guédon, A. Litvak, A. Pajor and N. TomczakJaegermann, Condition number of a square matrix with i.i.d. columns drawn from a convex body. Proc. Amer. Math. Soc. 140 (2012), 987998. pdf file
12. With A. Litvak, A. Pajor and N. TomczakJaegermann, Sharp bounds on the rate of convergence of the empirical covariance matrix. Comptes Rendus Mathematique, Volume 349, Issues 34, February 2011, Pages 195200. arXiv version
13. On the MarchenkoPastur and circular laws for some classes of random matrices with dependent entries Electronic Journal of Probability, Vol. 16 (2011) 10651095.
14. With R. Latała, A. Litvak, A. Pajor and N. TomczakJaegermann, Geometry of logconcave Ensembles of random matrices and approximate reconstruction. Comptes Rendus Mathematique, Volume 349, Issues 1314, July 2011, Pages 783786. This is an announcement (without proofs) of the results contained in the following two articles. arXiv version
15. With R. Latała, A. Litvak, A. Pajor and N. TomczakJaegermann, Chevet type inequality and norms of submatrices. Studia Math. 210 (2012), 3556. arXiv version
16. With R. Latała, A. Litvak, A. Pajor and N. TomczakJaegermann, Tail estimates for norms of sums of logconcave random vectors (To appear in Proceedings of the London Mathematical Society). arXiv version
17. With P. Miłoś, CLT for OrnsteinUhlenbeck branching particle system. Electronic Journal of Probability, Vol 20, Article 42 (2015). arXiv version
18. With P. Miłoś, Ustatistics of OrnsteinUhlenbeck branching particle system. Journal of Theoretical Probability. Volume 27, Issue 4, 10711111 (2014).
19. With W. Bednorz, Exponential Concentration Inequalities for Additive Functionals of Markov Chains. ESAIM: PS, 19, 440481 (2015). arXiv version
20. With R. Latała, A. Litvak, K. Oleszkiewicz, A. Pajor and N. TomczakJaegermann, A Short Proof of Paouris' Inequality Canadian Mathematical Bulletin 57, 38 (2014). arXiv version
21. With O. Guédon, R. Latała, A. Litvak, K. Oleszkiewicz, A. Pajor and N. TomczakJaegermann, Moment estimates for convex measures. Electronic Journal of Probability, Vol. 17, Article 1
22. The operator norm of random rectangular Toeplitz matrices. High Dimensional Probability VI, The Banff Volume. Progress in Probability, Vol. 66, 247260 (2013). .pdf file
23. Some remarks on the DozierSilverstein Theorem for random matrices with dependent entries. Random Matrices: Theory and Applications, Volume 02, Issue 02, April 2013
24. With D. Chafaï, Circular law for random matrices with unconditional logconcave distribution. Communications in Contemporary Mathematics Volume 17, Issue 04 (2015). arXiv version
25. With P. Wolff, Concentration inequalities for nonLipschitz functions with bounded derivatives of higher order. Probability Theory and Related Fields. Vol. 162, Issue 3, 531586 (2015). arXiv version
26. With W. Bednorz, Some remarks on MCMC estimation of spectra of integral operators. Bernoulli, Vol. 21, No. 4, 20732092 (2015). arXiv version
27. With D. Chafaï and P. Wolff, Circular law for random matrices with exchangeable entries. Random Structures and algorithms, Volume 48, Issue 3 (2016). arXiv version
28. With W. Bednorz, Orlicz integrability of additive functionals of Harris ergodic Markov chains. High Dimensional Probability VII, Cargèse Volume, Progress in Probability, vol 71. Birkhäuser, Cham, 295326 (2016). arXiv version
29. A note on the HansonWright inequality for random vectors with dependencies. Electron. Commun. Probab. Volume 20 (2015), paper no. 72. arXiv version
30. With R. Latała, Z. Puchała, K. Życzkowski, Asymptotic entropic uncertainty relations. J. Math. Phys. 57, 032204 (2016). arXiv version
31. With M. Strzelecki, Modified logSobolev inequalities for convex functions on the real line. Sufficient conditions. Studia Mathematica 230 (2015), 5993. arXiv version
32. With W. Bednorz and P. Wolff, Moment estimates implied by modified logSobolev inequalities. ESAIM Probab. Stat. 21 (2017), 467494. arXiv version
33. A note on the sample complexity of the ErSpUD algorithm by Spielman, Wang and Wright for exact recovery of sparsely used dictionaries. Journal of Machine Learning Research, 17(177):118 (2016). arXiv version
34. Metric and classical fidelity uncertainty relations for random unitary matrices. Journal of Physics A: Mathematical and Theoretical, Volume 50, Number 10 (2017). arXiv version
35. On the convex Poincaré inequality and weak transportation inequalities. To appear in Bernoulli. arXiv version
36. Random nonAbelian Gcirculant matrices. Spectrum of random convolution operators on large finite groups (preprint). arXiv version
37. With M. Kotowski and P. Miłoś, Phase transition for the interchange and quantum Heisenberg models on the Hamming graph (preprint). arXiv version
38. With M. Kotowski, B. Polaczyk and M. Strzelecki, A note on concentration for polynomials in the Ising model (preprint) arXiv version .
39. With R. Latała and R. Meller, HansonWright inequality in Banach spaces arXiv version
2016 Habilitation, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw. Random matrices with dependent coefficients
2007 PhD in Mathematics, Institute of Mathematics, Polish Academy of Sciences. Thesis: Ustatistics. Inequalities and laws of the iterated logarithm. Advisor: Prof. Rafał Latała.
2003 MSc in Mathematics, University of Warsaw and Vrije Universiteit van Amsterdam (within the Joint Master's Programme). Master's thesis: The entropy method and concentration of measure in product spaces (at the University of Warsaw: "Koncentracja miary") written under supervision of prof. Rafał Latała (Poland) and prof. Aad van der Vaart (the Netherlands).
2001 Bachelor's thesis at the University of Warsaw: "Symetryzacje dwupunktowe i radialne, a nierówność izoperymetryczna" (Two point and radial symmetrizations and the isoperimetric inequality) written under supervision of prof. Rafał Latała
A member of the Polish Mathematical Society
2012 Scholarship for Outstanding Young Scientists, Ministry of Science and Higher Education
2010 Nomination for the International Banach Prize
2010 Wojtek Pulikowski Lectureship at the Adam Mickiewicz University in Poznań
2010 Foundation for Polish Science Scholarship (special distinction)
2009 Kazimierz Kuratowski Award
2009 Foundation for Polish Science Scholarship
2008 Polish Mathematical Society Award for Young Mathematicians
2007 Marek Wacławek Foundation Award
2007 Stanisław Saks Scholarship given by the Foundation of Mathematicians of the City of Wrocław
19961998 Polish Children Found Scholarship
2010 A four month postdoctoral stay at the Fields Institute in Toronto
20072008 A one year postdoctoral stay at the Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada (Pacific Institute for the Mathematical Sciences Postdoctoral Fellowship)
2006 A threemonth stay at the Institut Henri Poincaré in Paris during the special trimester "Phenomena in High Dimensions" (Marie Curie Fellowship)
2003 An eightmonth stay at Vrije Universiteit van Amsterdam, Faculty of Science, Department of Mathematics within the Joint Master's Programme of VUA and University of Warsaw
2001 A fourmonth stay at Vrije Universiteit van Amsterdam, Faculty of Science, Department of Mathematics within the Socrates Erasmus Exchange Programme.
20122015 A member of the Kuratowski Award Jury (vice chairman in 2014, chairman in 2015)
2013 A member of the panel of experts in the Fuga grant competition (National Science Center, Poland)
2014 A member of the panel of experts in the Etiuda grant competition (National Science Center, Poland)
2017 A member of the panel of experts of the National Science Center, Poland
20182020 A member of the Jury of the Wacław Sierpiński Medal and Lecture
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Probability in Banach Spaces by M. Ledoux and M. Talagrand at M. Talagrand's home page
Markov Chains and Stochastic Stability by S.P. Meyn and R. L. Tweedie
An Introduction to Random Matrices by G. Anderson, A. Guionnet and O. Zeitouni at O. Zeitouni's home page
Expander Graphs and their Applications by S. Hoory, N. Linial and A. Wigderson at A. Wigderson's web page
Martingales in Banach Spaces by G. Pisier
RiemannHilbert Problems and Multiple Orthogonal Polynomials by Arno Kuijlaars
What's new by Terence Tao
Combinatorics and more by Gil Kalai
Timothy Gowers' Weblog
Libres pensées... by Djalil Chafaï
Almost sure by George Lowther
N is a Number A Portrait of Paul Erdős
Przestrzenie Banacha  a movie about Stefan Banach (in Polish)