Related papers: Some Hoeffding- and Bernstein-type Concentration I…
This paper provides a systematic study of fundamental combinatorial properties of one-dimensional, two-sided infinite simple Toeplitz subshifts. Explicit formulas for the complexity function, the palindrome complexity function and the…
Interpolation inequalities in Triebel-Lizorkin-Lorentz spaces and Besov-Lorentz spaces are studied for both inhomogeneous and homogeneous cases. First we establish interpolation inequalities under quite general assumptions on the parameters…
In this paper, we establish an extension of a noncommutative Bennett inequality with a parameter $1\leq r\leq2$ and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative…
In this paper, we derive a new version of Hanson-Wright inequality for a sparse bilinear form of sub-Gaussian variables. Our results are generalization of previous deviation inequalities that consider either sparse quadratic forms or dense…
In this short note we derive concentration inequalities for the empirical absolute moments of square symmetric matrices with independent symmetrically distributed +/-1 entries. Most of the previous results of this type are limited to…
In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary…
We extend the Moser-Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schr\"odinger operators on bounded domains.
In this note we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Also a few Beurling type hitting estimates are obtained for the random walk on discretizations of…
We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the…
A new characterization of the exponential type Orlicz spaces generated by the functions $\exp(|x|^p)-1$ ($p\ge 1$) is given. We define norms for centered random variables belonging to these spaces. We show equivalence of these norms with…
We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such…
We consider Gibbs measures on the configuration space $S^{\mathbb{Z}^d}$, where mostly $d\geq 2$ and $S$ is a finite set. We start by a short review on concentration inequalities for Gibbs measures. In the Dobrushin uniqueness regime, we…
Reverse H\"{o}lder inequalities for a class of functions on a probability space constitute an important tool in Analysis in Probability. After revisiting how a (modified) log-Sobolev inequality can be used to derive reverse H\"{o}lder…
We study various generalizations of concentration of measure on the unit sphere, in particular by means of log-Sobolev inequalities. First, we show Sudakov-type concentration results and local semicircular laws for weighted random matrices.…
We prove a concentration inequality which asserts that, under some mild regularity conditions, every random variable defined on the product of sufficiently many probability spaces exhibits pseudorandom behavior.
Incomplete U-statistics have been proposed to accelerate computation. They use only a subset of the subsamples required for kernel evaluations by complete U-statistics. This paper gives a finite sample bound in the style of Bernstein's…
By using coupling arguments, Harnack type inequalities are established for a class of stochastic (functional) differential equations with multiplicative noises and non-Lipschitzian coefficients. To construct the required couplings, two…
In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These inequalities extend the corresponding inequalities for independent random variables. Our conditions…
We obtain Rosenthal-type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremisers in log-concave settings when the moments of summands are…
We show that any probability measure satisfying a Matrix Poincar\'e inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carr\'e du champ…