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A tail inequality for suprema of unbounded empirical processes with applications to Markov chains

- R. Adamczak
- Mathematics
- 19 September 2007

We present a tail inequality for suprema of empirical processes generated by variables with finite $\psi_\alpha$ norms and apply it to some geometrically ergodic Markov chains to derive similar… Expand

Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles

- R. Adamczak, A. Litvak, A. Pajor, N. Tomczak-Jaegermann
- Mathematics
- 13 March 2009

Let K be an isotropic convex body in Rn. Given e > 0, how many independent points Xi uniformly distributed on K are neededfor the empirical covariance matrix to approximate the identity up to e with… Expand

Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order

- R. Adamczak, P. Wolff
- Mathematics
- 5 April 2013

Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Latała we provide a concentration inequality for not necessarily Lipschitz functions… Expand

Moment inequalities for U-statistics

- R. Adamczak
- Mathematics
- 1 June 2005

We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the… Expand

A note on the Hanson-Wright inequality for random vectors with dependencies

- R. Adamczak
- Mathematics
- 30 September 2014

We prove that quadratic forms in isotropic random vectors $X$ in $\mathbb{R}^n$, possessing the convex concentration property with constant $K$, satisfy the Hanson-Wright inequality with constant… Expand

Restricted Isometry Property of Matrices with Independent Columns and Neighborly Polytopes by Random Sampling

- R. Adamczak, A. Litvak, A. Pajor, N. Tomczak-Jaegermann
- Mathematics
- 30 April 2009

This paper considers compressed sensing matrices and neighborliness of a centrally symmetric convex polytope generated by vectors ±X1,…,±XN∈ℝn, (N≥n). We introduce a class of random sampling matrices… Expand

CLT for Ornstein-Uhlenbeck branching particle system

- R. Adamczak, Piotr Milo's
- Mathematics
- 19 November 2011

In this paper we consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a… Expand

Sharp bounds on the rate of convergence of the empirical covariance matrix

- R. Adamczak, A. Litvak, A. Pajor, N. Tomczak-Jaegermann
- Mathematics
- 1 December 2010

On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries

- R. Adamczak
- Mathematics
- 6 February 2011

In the first part of the article we prove limit theorems of Marchenko-Pastur type for the average spectral distribution of random matrices with dependent entries satisfying a weak law of large… Expand

A Few Remarks on the Operator Norm of Random Toeplitz Matrices

- R. Adamczak
- Mathematics, Computer Science
- 21 March 2008

We present some results concerning the almost sure behavior of the operator norm of random Toeplitz matrices, including the law of large numbers for the norm, normalized by its expectation (in the… Expand

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