Related papers: Quantitative Versions of the Two-dimensional Gauss…
Let $\Sigma$ be a strictly convex, compact patch of a $C^2$ hypersurface in $\mathbb{R}^n$, with non-vanishing Gaussian curvature and surface measure $d\sigma$ induced by the Lebesgue measure in $\mathbb{R}^n$. The Mizohata--Takeuchi…
The aim of this paper is to establish the asymptotic behavior of the mutual influence of the Gini index and the poverty measures by using the Gaussian fields described in Mergane and Lo(2013). The results are given as representation…
In this article we review the standard versions of the Central and of the Levy-Gnedenko Limit Theorems, and illustrate their application to the convolution of independent random variables associated with the distribution known as…
Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a…
We provide a proof to a recent conjecture by Forrester [2014 J. Phys. A: Math. Theor. 47, 065202] regarding the algebraic and arithmetic structure of Meijer G-functions which appear in the expression for probability of all eigenvalues real…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
Let $n\ge 2$ and $g_{\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, \begin{align*} g_{\lambda}^{*}(f)(x) =\bigg(\iint_{\mathbb R^{n+1}_{+}}…
We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…
This paper proposes a reformulation of the Riemann Xi function in order to investigate its properties. The reformulated function, which depicts the Xi function as the weighted sum of incomplete gamma functions, is validated, and a number of…
The Gauss hypergeometric functions 2F1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers. It is shown that in the case of integer and/or…
We consider differences of one- and two-variable finite products and provide combinatorial proofs of the nonnegativity of certain coefficients. Since the products may be interpreted as generating functions for certain integer partitions,…
Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting…
We consider the ratio of two Gauss hypergeometric functions with real parameters shifted by arbitrary integers. We find a formula for the jump of this ratio over the branch cut in terms of a real hypergeometric polynomial, the beta density…
We find two-sided inequalities for the generalized hypergeometric function of the form ${_{q+1}}F_{q}(-x)$ with positive parameters restricted by certain additional conditions. Both lower and upper bounds agree with the value of…
Refining some results of S. S. Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is…
We introduce and document a class of probability distributions, called bilateral generalized inverse Gaussian (BGIG) distributions, that are obtained by convolution of two generalized inverse Gaussian distributions supported by the positive…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds $(B,g_B)$ and $(F,g_F)$ furnished with metrics of the form $c^{2}g_B \oplus w^2 g_F$ and, in particular, of the type $w^{2 \mu}g_B \oplus w^2 g_F$,…
We study pseudo-Riemannian Einstein manifolds which are conformally equivalent with a metric product of two pseudo-Riemannian manifolds. Particularly interesting is the case where one of these manifolds is 1-dimensional and the case where…
Context. In previous work, we developed a quasi-Gaussian approximation for the likelihood of correlation functions, which, in contrast to the usual Gaussian approach, incorporates fundamental mathematical constraints on correlation…