Related papers: On normal approximations to symmetric hypergeometr…

Let X be a normed space. A subset A of X is approximately convex if $d(ta+(1-t)b,A) \le 1$ for all $a,b \in A$ and $t \in [0,1]$ where $d(x,A)$ is the distance of $x$ to $A$. Let $\Co(A)$ be the convex hull and $\diam(A)$ the diameter of…

Under the Kolmogorov--Smirnov metric, an upper bound on the rate of convergence to the Gaussian distribution is obtained for linear statistics of the matrix ensembles in the case of the Gaussian, Laguerre, and Jacobi weights. The main lemma…

This article presents a new proof of the rate of convergence to the normal distribution of sums of independent, identically distributed random variables in chi-square distance, which was also recently studied in \cite{BobkovRenyi}. Our…

We establish a connection between the $L^{q}$-spectrum of a Borel measure $\nu $ on the $m$-dimensional unit cube and the approximation order of Kolmogorov diameters of the unit sphere with respect to Sobolev norms in $L_{\nu }^{p}$. This…

The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace normal approximation in order to give an estimate at the tail…

In this paper, order estimates for the Kolmogorov $n$-widths of an intersection of a family of balls in a mixed norm in the space $l^{m,k}_{q,\sigma}$ with $2\le q, \, \sigma <\infty$, $n\le mk/2$ are obtained.

We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev and Besov norms in $L_{p}$-spaces on compact Riemannian manifolds. The proofs rely on estimates for the near-diagonal localization of the…

This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf…

A pair of probability distributions over $\{0,1\}^n$ is said to be $(k,\delta)$-wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $\delta$. Previous works introduced this concept and study when…

In this paper, we apply the so-called Alexandrov-Bakelman-Pucci (ABP) method to establish some geometric inequalities. We first prove a logarithmic Sobolev inequality for closed $n$-dimensional minimal submanifolds $\Sigma$ of $\mathbb…

The small mass limit of the Langevin equation perturbed by $\alpha$-stable L\'{e}vy noise is considered by rewriting it in the form of slow-fast system, and spliting the fast component into three parts, where $\alpha\in(1,2)$. By exploring…

We consider the following second-order stochastic differential equation on $\mathbb{R}^{2d}$: \begin{equation*} dX_t^m=Y_t^mdt, \quad mdY_t^m=b(X_t^m)dt+\sigma(X_t^m)dB_t-Y^m_tdt, \end{equation*} where $X^m_t$ and $Y^m_t$ represent the…

The Bregman distance is a central tool in convex optimization, particularly in first-order gradient descent and proximal-based algorithms. Such methods enable optimization of functions without Lipschitz continuous gradients by leveraging…

We study the rate of convergence of the empirical spectral distribution of products of independent non-Hermitian random matrices to the power of the Circular Law. The distance to the deterministic limit distribution will be measured in…

Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…

In this paper, we derive the first order approximate symmetries for the Harry Dym equation by the method of approximate transformation groups proposed by Baikov, Gaszizov and Ibragimov. Moreover, we investigate the structure of the Lie…

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by infinitely divisible laws may be transferred to the estimation of the closeness of…

We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting…

We study the asymptotic distributions of the number of crossings and the number of simple chords in a random chord diagram. Using size-bias coupling and Stein's method, we obtain bounds on the Kolmogorov distance between the distribution of…

We consider the problem of generating pseudo-random matrices based on the similarity of their spectra to Wigner's semicircular law. We introduce the notion of an r-independent pseudo-Wigner matrix ensemble and prove closeness of the spectra…