Related papers: A note on gaussian distributions in R^n

Let $A$ be an $n\times n$ random matrix with independent rows $R_1(A),\dots,R_n(A)$, and assume that for any $i\leq n$ and any three-dimensional linear subspace $F\subset {\mathbb R}^n$ the orthogonal projection of $R_i(A)$ onto $F$ has…

These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Banach spaces. They originated as the notes for a topics course…

Let I be a compact d-dimensional manifold, let X:I\to R be a Gaussian process with regular paths and let F_I(u), u\in R, be the probability distribution function of sup_{t\in I}X(t). We prove that under certain regularity and nondegeneracy…

Mutual space-frequency distribution is proposed and it is shown that Wigner and Weyl distribution functions are only particular cases of these distribution. Mutual distribution for Gaussian signal is analytically obtained. The simple…

We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a…

Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to…

Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a…

Gaussian quasi-invariant measures on groups of diffeomorphisms and loop groups G relative to dense subgroups G' were constructed. In the non-Archimedean case the wider class of measures was investigated, than in the real case. The cases of…

We use the spherical evolution approximation to investigate nonlinear evolution from the non-Gaussian initial conditions characteristic of the local f_nl model. We provide an analytic formula for the nonlinearly evolved probability…

We consider statistical mechanics models of continuous spins in a disordered environment. These models have a natural interpretation as effective interface models. It is well known that without disorder there are no interface Gibbs measures…

Let $\{f(t): t\in T\}$ be a smooth Gaussian random field over a parameter space $T$, where $T$ may be a subset of Euclidean space or, more generally, a Riemannian manifold. For any local maximum of $f(t)$ located at $t_0$ in the interior of…

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…

We introduce a location statistic for distributions on non-linear geometric spaces, the diffusion mean, serving as an extension and an alternative to the Fr\'echet mean. The diffusion mean arises as the generalization of Gaussian maximum…

A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to…

The present article derives the minimal number $N$ of observations needed to consider a Bayesian posterior distribution as Gaussian. Two examples are presented. Within one of them, a chi-squared distribution, the observable $x$ as well as…

Here we review the present status of modelling of and searching for primordial non-Gaussianity of cosmological perturbations. After introducing the models for non-Gaussianity generation during inflation, we discuss the search for…

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…

In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube…

The space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By…

Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with…