Related papers: Total variation distance estimates via $L^2$-norm …
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are…
Given two sets $x_1^{(1)},\ldots,x_{n_1}^{(1)}$ and $x_1^{(2)},\ldots,x_{n_2}^{(2)}\in\mathbb{R}^p$ (or $\mathbb{C}^p$) of random vectors with zero mean and positive definite covariance matrices $C_1$ and $C_2\in\mathbb{R}^{p\times p}$ (or…
We provide a refined explicit estimate of exponential decay rate of underdamped Langevin dynamics in $L^2$ distance, based on a framework developed in [1]. To achieve this, we first prove a Poincar\'{e}-type inequality with Gibbs measure in…
In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
In this note, we compute the probability that a two-dimensional symmetric random walk visits more vertices than expected, for deviations on scales between the mean behavior and linear growth.
The absolute separation of a polynomial is the minimum nonzero difference between the absolute values of its roots. In the case of polynomials with integer coefficients, it can be bounded from below in terms of the degree and the height…
We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on $\R$. The formula is given in terms of the $R$-transform of the first measure, and…
An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the $L^2$ norms of the gradients of the functions, where the…
We introduce two probabilistic models of random log-concave polynomials, the uniform model and the beta model, and study the asymptotic distribution of their zeros in the complex plane. In the uniform model, we show that the empirical root…
We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…
In this paper we prove asymptotic upper bounds on the variance of the number of vertices and missed area of inscribed random disc-polygons in smooth convex discs whose boundary is $C^2_+$. We also consider a circumscribed variant of this…
We formulate and discuss a conjecture concerning lower bounds for norms of log-concave vectors, which generalizes the classical Sudakov minoration principle for Gaussian vectors. We show that the conjecture holds for some special classes of…
We introduce some new indexes to measure the departure of any multivariate continuous distribution on non-negative orthant from a given reference one such the uncorrelated exponential model, similar to the relative Fisher dispersion indexes…
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…
Approximation by polynomials on a triangle is studied in the Sobolev space $W_2^r$ that consists of functions whose derivatives of up to $r$-th order have bounded $L^2$ norm. The first part aims at understanding the orthogonal structure in…
Popular measures of meta-analysis heterogeneity, such as $I^2$, cannot be considered measures of population heterogeneity since they are dependant on samples sizes within studies. The coefficient of variation (CV) recently introduced and…
Let $K \in \R^d$ be a convex body, and assume that $L$ is a randomly rotated and shifted integer lattice. Let $K_L$ be the convex hull of the (random) points $K \cap L$. The mean width $W(K_L)$ of $K_L$ is investigated. The asymptotic order…
In this paper we study the generalized Erdos-Falconer distance problems in the finite field setting. The generalized distances are defined in terms of polynomials, and various formulas for sizes of distance sets are obtained. In particular,…