Related papers: The total variation distance between high-dimensio…

This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…

In this paper we derive sharp lower and upper bounds for the covariance of two bounded random variables when knowledge about their expected values, variances or both is available. When only the expected values are known, our result can be…

We study the convergence in total variation distance for series of the form $$ S_{N}(c,Z)=\sum_{l=1}^{N}\sum_{i_{1}<\cdots<i_{l}}c(i_{1},...,i_{l})Z_{i_{1}}\cdots Z_{i_{l}}, $$ where $Z_{k},k\in {\mathbb{N}}$ are independent centered random…

In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low sample size setting. Our test statistics include the well-known energy distance and maximum mean discrepancy with…

We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…

We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…

Suppose $n$ independent random variables $X_1, X_2, \dots, X_n$ have zero mean and equal variance. We prove that if the average of $\chi^2$ distances between these variables and the normal distribution is bounded by a sufficiently small…

The dimer model on a planar bipartite graph can be viewed as a random surface measure. We study these fluctuations for a dimer model on the square grid with two different classes of weights and provide a condition for their equivalence. In…

We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the…

The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence one obtains an invariance principle for such polynomials. This generalizes known results concerning the total…

We establish general upper bounds on the Kolmogorov distance between two probability distributions in terms of the distance between these distributions as measured with respect to the Wasserstein or smooth Wasserstein metrics. These bounds…

Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…

We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu (1935) and Bhatia and Davis (2000) concerning measures on the line to several dimensions. This is…

We prove the four-dimensional Gaussian random vector maximum conjecture. This conjecture asserts that among all centered Gaussian random vectors $X=(X_1,X_2,X_3,X_4)$ with $E[X_i^2]=1$, $1\le i\le 4$, the expectation…

We present a joint-measurement uncertainty relation for a pair of mean square deviations of canonical variables averaged over Gaussian distributed quantum optical states. Our Bayesian formulation is free from the unbiasedness assumption,…

Sums of independent, bounded random variables concentrate around their expectation approximately as well a Gaussian of the same variance. Well known results of this form include the Bernstein, Hoeffding, and Chernoff inequalities and many…

We show that a lower bound for covariance of $\min(X_1,X_2)$ and $\max(X_1,X_2)$ is $\cov{X_1}{X_2}$ and an upper bound for variance of \\ $\min(X_2,\max(X,X_1))$ is $\var{X} + \var{X_1} +\var{X_2}$ generalizing previous results. We also…

Given two distinct datasets, an important question is if they have arisen from the the same data generating function or alternatively how their data generating functions diverge from one another. In this paper, we introduce an approach for…

We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random…

In this paper, we prove a local limit theorem for the ratio of the Poisson distribution to the Gaussian distribution with the same mean and variance, using only elementary methods (Taylor expansions and Stirling's formula). We then apply…