Related papers: High-dimensional limit theorems for random vectors…
Let $\ell \geq 2$ be an integer. For each $\eps >0$ remove from $\R^2$ the union of discs of radius $\eps$ centered at the integer lattice points $(m,n$, with $m\nequiv n\mod{\ell}$. Consider a point-like particle moving linearly at unit…
Q-balls are large bound-state systems of scalar particles, described classically through localized solutions of the equations of motion. Promoting the required stabilizing $U(1)$ symmetry to a gauge symmetry leads to gauged Q-balls, which…
A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…
The ball-constrained weighted maximin dispersion problem $(\rm P_{ball})$ is to find a point in an $n$-dimensional Euclidean ball such that the minimum of the weighted Euclidean distance from given $m$ points is maximized. We propose a new…
In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to…
Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We…
We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…
We give a complete description of the horofunction boundary of finite-dimensional $\ell_p$ spaces for $1\leq p\leq \infty$. We also study the variation norm on $\mathbb{R}^{\mathcal{N}}$, $\mathcal{N}=\{1,...,N\}$, and the corresponding…
This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…
Given a Coxeter system of large type we prove a non--commutative central limit theorem: After normalisation with the square root of n the characteristic function of the set of the first n generators tends in distribution to Wigners…
In this work, we provide a $(n/m)^{-1/2}$-rate finite sample Berry-Esseen bound for $m$-dependent high-dimensional random vectors over the class of hyper-rectangles. This bound imposes minimal assumptions on the random vectors such as…
We consider the $p$-generalized arithmetic-geometric mean inequality for vectors chosen randomly from the $\ell_p^n$-ball in $\mathbb{R}^n$. In this setting the inequality can be improved or reversed up to a respective scalar constant with…
A probabilistic representation for a class of weighted $p$-radial distributions, based on mixtures of a weighted cone probability measure and a weighted uniform distribution on the Euclidean $\ell_p^n$-ball, is derived. Large deviation…
Having its origin in theoretical computer science, the Kannan-Lov\'asz-Simonovits (KLS) conjecture is one of the major open problems in asymptotic convex geometry and high-dimensional probability theory today. In this work, we establish a…
This paper enhances the result of the work [G. Kozma, B. T\'oth, Ann. Probab. vol. 45 (2017) 4307-4347] . We prove the central limit theorem (in probability w.r.t. the environment) for the displacement of a random walker in divergence-free…
Let $\mathbf{X}^{(1)}_{n},\ldots,\mathbf{X}^{(m)}_{n}$, where $\mathbf{X}^{(i)}_{n}=(X^{(i)}_{1},\ldots,X^{(i)}_{n})$, $i=1,\ldots,m$, be $m$ independent sequences of independent and identically distributed random variables taking their…
We prove a central limit theorem for the Horvitz-Thompson estimator based on the Gram-Schmidt Walk (GSW) design, recently developed in Harshaw et al.(2022). In particular, we consider the version of the GSW design which uses randomized…
We study the $L^p-L^q$ boundedness of Bergman projector on the minimal ball. This improves an important result of \cite{MY} due to G. Mengotti and E. H. Youssfi.
The maximal hyperplane section of the $l_\infty^n$-ball, i.e. of the $n$-cube, is the one perpendicular to 1/sqrt 2 (1,1,0, ... ,0), as shown by Ball. Eskenazis, Nayar and Tkocz extended this result to the $l_p^n$-balls for very large $p…
The random polytope $K_n$, defined as the convex hull of $n$ points chosen uniformly at random on the boundary of a smooth convex body, is considered. Proofs for lower and upper variance bounds, strong laws of large numbers and central…