Related papers: A central limit theorem for random disc-polygons i…
We present a method to obtain upper bounds on covering numbers. As applications of this method, we reprove and generalize results of Rogers on economically covering Euclidean $n$-space with translates of a convex body, or more generally,…
In this note, we prove a central limit theorem for the mass distribution of random holomorphic sections associated with a sequence of positive line bundles endowed with $\mathscr{C}^3$ Hermitian metrics over a compact K\"{a}hler manifold.…
It is proved by Brendle in [4] that the equatorial disk $D^k$ has least area among $k$-dimensional free boundary minimal surfaces in the Euclidean ball $B^n$. By comparing the excess of free boundary minimal surfaces with the excess of the…
On a probability space $(\Omega, \mathcal F, \mathbb P)$ we consider two independent sequences $(a_k)_{k \geq 1}$ and $(b_k)_{k \geq 1}$ of i.i.d. random variables that are centered with unit variance and which admit a moment strictly…
Let $K$ be a convex body in $\mathbb{R}^n$ and $f : \partial K \rightarrow \mathbb{R}_+$ a continuous, strictly positive function with $\int\limits_{\partial K} f(x) d \mu_{\partial K}(x) = 1$. We give an upper bound for the approximation…
Let $f:[0,1)^d \to {\mathbb R}$ be an integrable function. An objective of many computer experiments is to estimate $\int_{[0,1)^d} f(x) dx$ by evaluating f at a finite number of points in [0,1)^d. There is a design issue in the choice of…
A discrete gradient model for interfaces is studied. The interaction potential is a non-convex perturbation of the quadratic gradient potential. Based on a representation for the finite volume Gibbs measure obtained via a renormalization…
The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$ are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the…
We consider a borderline case: the central limit theorem for a strictly stationary time series with infinite variance but a Gaussian limit. In the iid case a well-known sufficient condition for this central limit theorem is regular…
We investigate the asymptotic behavior of the $L_p$-distance between a monotone function on a compact interval and a smooth estimator of this function. Our main result is a central limit theorem for the $L_p$-error of smooth isotonic…
This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the…
We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) a certain random variable on the…
A classical result of Dowker (Bull. Amer. Math. Soc. 50: 120-122, 1944) states that for any plane convex body $K$ in the Euclidean plane, the areas of the maximum (resp. minimum) area convex $n$-gons inscribed (resp. circumscribed) in $K$…
In this paper we prove a uniform Fourier restriction estimate over the class of simple curves where the last coordinate function can be extended to a holomorphic function of bounded frequency in a sufficiently large disc. The proof is based…
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process.…
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
We study the long-range one-dimensional Riesz gas on the circle, a continuous system of particles interacting through a Riesz kernel. We establish near-optimal rigidity estimates on gaps valid at any scale. Leveraging these local laws…
We prove a Central Limit Theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.
The paper continues the author's research in the problem of quantitative investigation of basic curvelinear quasiinvariants of quasiconformal curves. It concerns polygons with infinite number of vertices and provides various distortion…