Related papers: Quadratic Forms in Gaussian Random Variables Theor…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but…
A strategy to address the inverse Galois problem over Q consists of exploiting the knowledge of Galois representations attached to certain automorphic forms. More precisely, if such forms are carefully chosen, they provide compatible…
The presented paper is devoted to statistical modeling of Gaussian scalar real random fields inside a three-dimensional sphere (ball). We propose a statistical model describing the spatial heterogeneity in a unit ball and a numerical…
Estimating the left tail of quadratic forms in Gaussian random vectors is of major practical importance in many applications. In this paper, we propose an efficient and robust importance sampling estimator that is endowed with the bounded…
This paper investigates the quadratic irrationals that arise as periodic points of the Gauss type shift associated to the odd continued fraction expansion. It is shown that these numbers, which we call O-reduced, when ordered by the length…
q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, in the range 1 < q < 3, the q-functions pass from the usual Gaussian form,…
By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to…
Dealing with quadratic payments, marginal probability is usually considered ideally constant, maybe for the sake of initial simplicity. Considering the voting scenario depicted in "Quadratic Payments: A Primer" by Vitalik Buterin, firstly…
Given a non-empty genus in $n$ dimensions with determinant $d$, we give a randomized algorithm that outputs a quadratic form from this genus. The time complexity of the algorithm is poly$(n,\log d)$; assuming Generalized Riemann Hypothesis…
Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…
For suitable pairs of diagonal quadratic forms in 8 variables we use the circle method to investigate the density of simultaneous integer solutions and relate this to the problem of estimating linear correlations among sums of two squares.
In this paper we define (empirical) quadratic variations for a Gaussian isotropic random field $f$ on a unit sphere as sums over equidistant increments on one single geodesic line on the surface of the sphere. We prove a noncentral limit…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zheng on the single variable case. As an application, for…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are…
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…
A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the…
The purpose of this article is to give a short introduction to the concept of quasi-unitary equivalence of quadratic forms and its consequences. In particular, we improve an estimate concerning the transitivity of quasi-unitary equivalence…