Related papers: Concentration Inequalities for Bounded Random Vect…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
The work is about homogenization for a type of multivalued Dirichlet-Neumann problems. First, we prove an average principle for general multivalued stochastic differential equations in the weak sense. Then for general forward-backward…
This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed…
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 property (SRP). Our result for SCP measures include…
We extend the theory of concentration inequalities to simple random tensors with heavy-tailed coefficients. Specifically, we consider the class of sub-Weibull distributions $\mathcal{S}_\alpha$ for $\alpha \in [1, 2]$. We establish…
Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…
We give a uniform estimate and an inequality for solutions of an equation with Dirichlet boundary condition.
In a companion article we have introduced a notion of multiscale functional inequalities for functions $X(A)$ of an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. These inequalities are multiscale weighted versions…
This article addresses an equidistribution problem concerning the zeros of systems of random holomorphic sections of positive line bundles on compact K\"{a}hler manifolds and random polynomials on $\mathbb{C}^{m}$ in the setting of the…
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
A generalization of Mercer inequality for h-convex function is presented. As application, a weighted generalization of triangle inequality is given.
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
A variant of the well-known Chebyshev inequality for scalar random variables can be formulated in the case where the mean and variance are estimated from samples. In this paper we present a generalization of this result to multiple…
The tails of the distribution of a mean zero, variance $\sigma^2$ random variable $Y$ satisfy concentration of measure inequalities of the form $\mathbb{P}(Y \ge t) \le \exp(-B(t))$ for $$ B(t)=\frac{t^2}{2( \sigma^2 + ct)} \quad \mbox{for…
In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…