Research articles

The main links below lead to journal versions of the articles. The arXiv versions may differ (in fact do differ) from the final ones.

1. Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses, Bulletin Polish Acad. Sci. Math. 53 (2005), 221-238. arXiv version

2. Moment Inequalities for U-statistics, Ann. Probab. 2006, Vol. 34, No. 6, 2288-2314. arXiv version

3. With R. Latała, The LIL for canonical U-statistics, Ann. Probab. 2008, Vol. 36, No. 3, 1023-1058. arXiv version

4. With R. Latała, The LIL for U-statistics in Hilbert spaces, J. Theoret. Probab. 21 (2008), 704-744. arXiv version

5. A tail inequality for suprema of unbounded empirical processes with applications to Markov chains, Electronic Journal of Probability, Vol. 13 (2008), 1000-1034.

6. A few remarks on the operator norm of random Toeplitz matrices, J. Theoret. Probab, Volume 23 (2010), Number 1, 85-108. arXiv version

7. With O. Guédon, A. Litvak, A. Pajor and N. Tomczak-Jaegermann, Smallest singular value of random matrices with independent columns, Comptes Rendus Mathematique Vol. 346, Issues 15-16, 2008, 853-856

8. With A. Litvak, A. Pajor and N. Tomczak-Jaegermann, Quantitative estimates of the convergence of the empirical covariance matrix in Log-concave Ensembles. J. Amer. Math. Soc. 23 (2010), 535-561. arXiv version

9. With A. Litvak, A. Pajor and N. Tomczak-Jaegermann, Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling. Constructive Approximation Vol. 34, No. 1, 61-88. arXiv version

10. With R. Latała, Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails. To appear in Annales de l’Institut Henri Poincaré. arXiv version

11. With O. Guédon, A. Litvak, A. Pajor and N. Tomczak-Jaegermann, Condition number of a square matrix with i.i.d. columns drawn from a convex body. To appear in Proc. Amer. Math. Soc. pdf file

12. With A. Litvak, A. Pajor and N. Tomczak-Jaegermann, Sharp bounds on the rate of convergence of the empirical covariance matrix. Comptes Rendus Mathematique Volume 349, Issues 3-4, February 2011, Pages 195-200. arXiv version

13. On the Marchenko-Pastur and circular laws for some classes of random matrices with dependent entries Electronic Journal of Probability, Vol. 16 (2011) 1065-1095.

14. With R. Latała, A.Litvak, A. Pajor and N. Tomczak-Jaegermann, Geometry of log-concave Ensembles of random matrices and approximate reconstruction (accepted for Comptes Rendus Mathematique). 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. Tomczak-Jaegermann, Chevet type inequality and norms of submatrices (submitted). arXiv version

16. With R. Latała, A.Litvak, A. Pajor and N. Tomczak-Jaegermann, Tail estimates for norms of sums of log-concave random vectors (submitted). arXiv version

17. With P. Miłoś, CLT for Ornstein-Uhlenbeck branching particle system. arXiv version

18. With P. Miłoś, U-statistics of Ornstein-Uhlenbeck branching particle system. arxiv version

19. With W. Bednorz, Orlicz integrability of additive functionals of Harris ergodic Markov chains. arxiv version

20. With W. Bednorz, Exponential Concentration Inequalities for Additive Functionals of Markov Chains, arxiv version

Others

1. Równania różniczkowe zwyczajne - lecture notes on ODE's by prof. Feliks Przytycki, which I had the honour to coedit (PL!). pdf

2. Master's thesis (or actually something in between of its Warsaw and Amsterdam version). pdf

3. Bachelor's thesis (PL). pdf