Related papers: On a characterization theorem in the space $\mathb…
In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known covariance and product…
The main aim of this note is to provide characterization theorems concerning real derivations. Among others the following implication will be verified: Assume that $\xi\colon \mathbb{R}\to \mathbb{R}$ is a given differentiable function and…
We consider random walks on the square lattice of the plane along the lines of Heyde (1982, 1993) and den Hollander (1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics.…
The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing…
We discuss a characterization of the centered Gaussian distribution which can be read from results of Archimedes and Maxwell, and relate it to Charles Stein's well-known characterization of the same distribution. These characterizations fit…
Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We…
We show that the Freiman--Ruzsa theorem, characterising finite sets with bounded doubling, leads to an alternative proof of a characterisation of Meyer sets, that is, relatively dense subsets of Euclidean spaces whose difference sets are…
In this paper we present a conditional principle of Gibbs type for independent nonidentically distributed random vectors. We obtain this result by performing Edgeworth expansions for densities of sums of independent random vectors.
We give counterexamples to a problem of M. Kac in the Scottish Book, which asks whether a certain nonlinear operation on two characteristic functions characterizes Laplace distributions, in analogy with the Cram\'er--L\'evy theorem for…
A $\phi$-exponential distribution is a generalization of an exponential distribution associated to functions $\phi$ in an appropriate class, and the space of $\phi$-exponential distributions has a dually flat structure. We study features of…
Learning of a smooth but nonparametric probability density can be regularized using methods of Quantum Field Theory. We implement a field theoretic prior numerically, test its efficacy, and show that the data and the phase space factors…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…
This paper derives a new strong Gaussian approximation bound for the sum of independent random vectors. The approach relies on the optimal transport theory and yields \textit{explicit} dependence on the dimension size $p$ and the sample…
We consider linear elliptic equations in divergence form with stationary random coefficients of integrable correlations. We characterize the fluctuations of a macroscopic observable of a solution to relative order $\frac{d}{2}$, where $d$…
We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of…
Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…
The Davis--Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on an eigenvalue separation condition between…
Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…
We prove that certain classical groups $G\subseteq {\rm GL}(d,\mathbb{R}^d)$ serve to characterize ordinary polynomials in $d$ real variables as elements of finite-dimensional subspaces of $C(\mathbb{R}^d)$ that are invariant by changes of…
In this article, we obtain the exact distribution of a linear combination of bilateral gamma (BG) random variables (r.v.s). Next, we discuss the distributional properties of the linear combination of BG r.v.s, including probability density…