Related papers: Gaussian Mills ratio is completely monotone

We investigate a convexity properties for normalized log moment generating function continuing a recent investigation of Chen of convex images of Gaussians. We show that any variable satisfying a ``Ehrhard-like'' property for its…

We investigate the continuous function $f$ defined by $$x\mapsto \sum_{\sigma\le_L x }2^{-K(\sigma)}$$ as a variant of Chaitin's Omega from the perspective of analysis, computability, and algorithmic randomness. Among other results, we…

We provide a new proof for maximal monotonicity of the subdifferential of a convex function.

In this paper, we prove that, if functions (concave) $\phi$ and (convex) $\psi$ satisfy certain conditions, the $L_{\phi}$ affine surface area is monotone increasing, while the $L_{\psi}$ affine surface area is monotone decreasing under the…

We study sampling properties of the zero set of the Gaussian entire function on Fock spaces. Firstly, we relax Seip and Wallst\'en's density and separation conditions for sampling sets on Fock spaces to obtain weighted inequalities for sets…

In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…

This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…

We present a self-contained proof of a uniform bound on multi-point correlations of trigonometric functions of a class of Gaussian random fields. It corresponds to a special case of the general situation considered in [Hairer-Xu], but with…

We show that Newton's method converges globally at a linear rate for objective functions whose Hessians are stable. This class of problems includes many functions which are not strongly convex, such as logistic regression. Our linear…

To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By…

Let $\mathfrak{q}>2$ be a prime number, $\chi$ a primitive Dirichlet character modulo $\mathfrak{q}$ and $f$ a primitive holomorphic cusp form or a Hecke-Maass cusp form of level $\mathfrak{q}$ and trivial nebentypus. We prove the subconvex…

Consider a H\"older continuous potential $\phi$ defined on the full shift $A^\nn$, where $A$ is a finite alphabet. Let $X\subset A^\nn$ be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$…

The average density of zeros for monic generalized polynomials, $P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the…

We study a new class of so-called rational-infinitely (or quasi-infinitely) divisible probability laws on the real line. The characteristic functions of these distributions are ratios of the characteristic functions of classical infinitely…

We consider the problem of characterizing all functions $f$ defined on the set of integers modulo $n$ with the property that an average of some $n$th roots of unity determined by $f$ is always an algebraic integer. Examples of such…

In the purely affine formulation of gravity, the gravitational field is represented by the symmetric part of the Ricci tensor of the affine connection. The classical electromagnetic field can be represented in this formulation by the second…

The authors establish the necessary and sufficient conditions under which certain combinations of Gaussian hypergeometric function and elementary function are monotone in the parameter, which generalize the recent results of generalized…

This work has a purpose to collect selected facts about the completely monotone (CM) functions that can be found in books and papers devoted to different areas of mathematics. We opted for lesser known ones, and for those which may help…

Let $n\ge2$ and let $\Phi\colon\mathbb{R}^n\to[0,\infty)$ be a positively $1$-homogeneous and convex function. Given two convex bodies $A\subset B$ in $\mathbb{R}^n$, the monotonicity of anisotropic $\Phi$-perimeters holds, i.e.…

We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…