Radosław Adamczak

activity

20052026

most citedQuantitative estimates of the convergence of the empirical covariance matrix in Log-concave Ensembles

117 citations · 484 across the 43 of their papers we have counts for

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45 papers · 1 filter

math.PR2026

Stability under mixtures of transportation inequalities and restricted log-Sobolev inequalities

Radosław Adamczak, Dominik Kutek, Michał Strzelecki

We prove results about stability under mixtures for transport--entropy inequalities and restricted functional inequalities of Poincaré and log-Sobolev type. We treat Talagrand ineq…

math.PR2025

Concentration of measure for non-linear random matrices with applications to neural networks and non-commutative polynomials

Radosław Adamczak

We prove concentration inequalities for several models of non-linear random matrices. As corollaries we obtain estimates for linear spectral statistics of the conjugate kernel of n…

math.PR2025★ 1 cited

Matrix concentration inequalities for dependent binary random variables

Radosław Adamczak, Ioannis Kavvadias

We prove Bernstein-type matrix concentration inequalities for linear combinations with matrix coefficients of binary random variables satisfying certain $ℓ_{\infty}$ -independence…

math.PR2024

Exponential inequalities and laws of the iterated logarithm for multiple Poisson--Wiener integrals and Poisson $U$ -statistics

Radosław Adamczak, Dominik Kutek

We prove tail and moment inequalities for multiple stochastic integrals on the Poisson space and for Poisson $U$ -statistics. We use them to demonstrate the Law of the Iterated Loga…

math.PR2024

The global and local limit of the continuous-time Mallows process

Radosław Adamczak, Michał Kotowski

Continuous-time Mallows processes are processes of random permutations of the set ${1, \dots, n}$ whose marginal at time $t$ is the Mallows distribution with parameter $t$ . Rece…

math.PR2023

On Orlicz spaces satisfying the Hoffmann-Jørgensen inequality

Radosław Adamczak, Dominik Kutek

Building on Talagrand's proof of the Hoffmann-Jørgensen inequality for $L_{p}$ spaces and its version for the exponential Orlicz spaces we provide a full characterization of Orlicz f…

math.PR2022

Limit theorems for the volumes of small codimensional random sections of $ℓ_{p}^{n}$ -balls

Radosław Adamczak, Peter Pivovarov, Paul Simanjuntak

We establish Central Limit Theorems for the volumes of intersections of $B_{p}^{n}$ (the unit ball of $ℓ_{p}^{n}$ ) with uniform random subspaces of codimension $d$ for fixed $d$ and $…

math.PR2021

Norms of structured random matrices

Radosław Adamczak, Joscha Prochno, Marta Strzelecka +1

For $m, n \in N$ let $X = (X_{ij})_{i \leq m, j \leq n}$ be a random matrix, $A = (a_{ij})_{i \leq m, j \leq n}$ a real deterministic matrix, and $X_{A} = (a_{ij} X_{ij})_{i \leq m, j \leq n}$ …

math.PR2021

Concentration inequalities for some negatively dependent binary random variables

Radosław Adamczak, Bartłomiej Polaczyk

We investigate concentration properties of functions of random vectors with values in the discrete cube, satisfying the stochastic covering property (SCP) or the strong Rayleigh pr…

math.PR2020★ 13 cited

Modified log-Sobolev inequalities, Beckner inequalities and moment estimates

Radosław Adamczak, Bartłomiej Polaczyk, Michał Strzelecki

We prove that in the context of general Markov semigroups Beckner inequalities with constants separated from zero as $p \to 1^{+}$ are equivalent to the modified log Sobolev inequalit…

math.PR2020★ 5 cited

Moments of Gaussian chaoses in Banach spaces

Radosław Adamczak, Rafał Latała, Rafał Meller

We derive moment and tail estimates for Gaussian chaoses of arbitrary order with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it h…

math.PR2019

On almost sure convergence of random variables with finite chaos decomposition

Radosław Adamczak

Under mild conditions on a family of independent random variables $(X_{n})$ we prove that almost sure convergence of a sequence of tetrahedral polynomial chaoses of uniformly bounded…

math.PR2018★ 10 cited

Hanson-Wright inequality in Banach spaces

Radosław Adamczak, Rafał Latała, Rafał Meller

We discuss two-sided bounds for moments and tails of quadratic forms in Gaussian random variables with values in Banach spaces. We state a natural conjecture and show that it holds…

math.PR2018★ 9 cited

A note on concentration for polynomials in the Ising model

Radosław Adamczak, Michał Kotowski, Bartłomiej Polaczyk +1

We present precise multilevel exponential concentration inequalities for polynomials in Ising models satisfying the Dobrushin condition. The estimates have the same form as two-sid…

math.PR2018★ 8 cited

Phase transition for the interchange and quantum Heisenberg models on the Hamming graph

Radosław Adamczak, Michał Kotowski, Piotr Miłoś

We study a family of random permutation models on the Hamming graph $H (2, n)$ (i.e., the $2$ -fold Cartesian product of complete graphs), containing the interchange process and the c…

math.PR2017

Random non-Abelian G-circulant matrices. Spectrum of random convolution operators on large finite groups

Radosław Adamczak

We analyse the limiting behavior of the eigenvalue and singular value distribution for random convolution operators on large (not necessarily Abelian) groups, extending the results…

math.PR2017★ 9 cited

On the convex Poincaré inequality and weak transportation inequalities

Radosław Adamczak, Michał Strzelecki

We prove that for a probability measure on $R^{n}$ , the Poincaré inequality for convex functions is equivalent to the weak transportation inequality with a quadratic-linear…

math.PR2016★ 9 cited

A note on the sample complexity of the Er-SpUD algorithm by Spielman, Wang and Wright for exact recovery of sparsely used dictionaries

Radosław Adamczak

We consider the problem of recovering an invertible $n \times n$ matrix $A$ and a sparse $n \times p$ random matrix $X$ based on the observation of $Y = A X$ (up to a scaling and pe…

math.PR2015

Moment estimates implied by modified log-Sobolev inequalities

Radosław Adamczak, Witold Bednorz, Paweł Wolff

We study a class of logarithmic Sobolev inequalities with a general form of the energy functional. The class generalizes various examples of modified logarithmic Sobolev inequaliti…

math.PR2015★ 5 cited

Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

Radosław Adamczak, Michał Strzelecki

We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the class…

math.PR2014★ 1 cited

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

Radosław Adamczak

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

math.PR2014★ 40 cited

Circular law for random matrices with exchangeable entries

Radosław Adamczak, Djalil Chafaï, Paweł Wolff

An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infi…

math.PR2013★ 8 cited

Some remarks on MCMC estimation of spectra of integral operators

Radosław Adamczak, Witold Bednorz

We prove a law of large numbers for empirical approximations of the spectrum of a kernel integral operator by the spectrum of random matrices based on a sample drawn from a Markov…

math.PR2013★ 2 cited

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

Radosław Adamczak, Paweł Wolff

Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Latała we provide a concentration inequality for non-necessarily Li…

Stability under mixtures of transportation inequalities and restricted log-Sobolev inequalities

Concentration of measure for non-linear random matrices with applications to neural networks and non-commutative polynomials

Matrix concentration inequalities for dependent binary random variables

Exponential inequalities and laws of the iterated logarithm for multiple Poisson--Wiener integrals and Poisson U-statistics

The global and local limit of the continuous-time Mallows process

On Orlicz spaces satisfying the Hoffmann-Jørgensen inequality

Limit theorems for the volumes of small codimensional random sections of ℓpn​-balls

Norms of structured random matrices

Concentration inequalities for some negatively dependent binary random variables

Modified log-Sobolev inequalities, Beckner inequalities and moment estimates

Moments of Gaussian chaoses in Banach spaces

On almost sure convergence of random variables with finite chaos decomposition

Hanson-Wright inequality in Banach spaces

A note on concentration for polynomials in the Ising model

Phase transition for the interchange and quantum Heisenberg models on the Hamming graph

Random non-Abelian G-circulant matrices. Spectrum of random convolution operators on large finite groups

On the convex Poincaré inequality and weak transportation inequalities

A note on the sample complexity of the Er-SpUD algorithm by Spielman, Wang and Wright for exact recovery of sparsely used dictionaries

Moment estimates implied by modified log-Sobolev inequalities

Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

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

Circular law for random matrices with exchangeable entries

Some remarks on MCMC estimation of spectra of integral operators

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

Exponential inequalities and laws of the iterated logarithm for multiple Poisson--Wiener integrals and Poisson $U$ -statistics

Limit theorems for the volumes of small codimensional random sections of $ℓ_{p}^{n}$ -balls