Related papers: Gaussian Zonoids, Gaussian determinants and Gaussi…

We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…

Zonoids are Hausdorff limits of zonotopes, while zonotopes are convex polytopes defined as the Minkowski sums of finitely many segments. We present a combinatorial framework that links the study of mixed volumes of zonoids (a topic that has…

We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumption of invariance. These include Gaussian matrices with…

Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical…

Inspired by Milman's recent observation, we prove that the Gaussian correlation inequality holds for convex sets having the same barycenter, and especially for centered ones. This gives an affirmative answer to the problem proposed by…

This tutorial focuses on the fundamental architectures of Variational Autoencoders (VAE) and Generative Adversarial Networks (GAN), disregarding their numerous variations, to highlight their core principles. Both VAE and GAN utilize simple…

Zeros of many ensembles of polynomials with random coefficients are asymptotically equidistributed near the unit circumference. We give quantitative estimates for such equidistribution in terms of the expected discrepancy and expected…

We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…

In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…

In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…

In a recent paper the author obtained optimal bounds for the strong Gaussian approximation of sums of independent $\R^d$-valued random vectors with finite exponential moments. The results may be considered as generalizations of well-known…

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…

A known result in random matrix theory states the following: Given a random Wigner matrix $X$ which belongs to the Gaussian Orthogonal Ensemble (GOE), then such matrix $X$ has an invariant distribution under orthogonal conjugations. The…

Suppose X is a random vector, that is distributed uniformly in some n-dimensional convex set. It was conjectured that when the dimension n is very large, there exists a non-zero vector u, such that the distribution of the real random…

Gaussian fields $(g_x)$ on $\mathbb{Z}_q^d$ are constructed from a class of reversible long range random walks $(X_t)_{t\in \mathbb{N}}$ on $\mathbb{Z}_q^d$ in arXiv:2510.22554. The construction is from taking the covariance function of…

Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…

To any $n$-dimensional random vector $X$ we may associate its $L_p$-centroid body ${\cal Z}_p(X)$ and the corresponding norm. We formulate a conjecture concerning the bound on the ${\cal Z}_p(X)$-norm of $X$ and show that it holds under…

Variational autoencoders (VAE) often use Gaussian or category distribution to model the inference process. This puts a limit on variational learning because this simplified assumption does not match the true posterior distribution, which is…

Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…

We consider the problem $(\rm P)$ of exactly fitting an ellipsoid (centered at $0$) to $n$ standard Gaussian random vectors in $\mathbb{R}^d$, as $n, d \to \infty$ with $n / d^2 \to \alpha > 0$. This problem is conjectured to undergo a…