Related papers: Zeros of random functions generated with de Brange…
This article studies the zeros of Dedekind zeta functions. In particular, we establish a smooth explicit formula for these zeros and we derive an effective version of the Deuring-Heilbronn phenomenon. In addition, we obtain an explicit…
We are interested in the differential equations satisfied by the density of the Geometric Stable processes $\mathcal{G}_{\alpha}^{\beta}=\left\{\mathcal{G}_{\alpha}^{\beta}(t);t\geq 0\right\} $, with stability \ index $% \alpha \in (0,2]$…
We study the instantons (or bounces) in the Brown-Teitelboim (BT) mechanism of relaxation of cosmological constant which is a cosmological version of the Schwinger mechanism. The BT mechanism is a false vacuum decay of (A)dS$_{d+1}$ (and…
In this article, we investigate the condensation phenomena for a class of nonreversible zero-range processes on a fixed finite set. By establishing a novel inequality bounding the capacity between two sets, and by developing a robust…
We systematically analyse the nuclear moments of inertia determined within the Skyrme and Gogny density functional theories. The time-odd mean fields generated by collective rotation are self-consistently determined by a novel exact…
We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially…
In the Hardy spaces $H^1$ and $H^\infty$, there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems when $H^1$ (resp., $H^\infty$) gets replaced by the…
We study random iterations of averaged operators in Hilbert spaces and prove that the associated residuals converge exponentially fast, both in expectation and almost surely. Our results provide quantitative bounds in terms of a single…
This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…
The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…
Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…
We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…
This paper provides a study of problems related to Hardy spaces left by G.\,Weiss in \cite{We}. First, We will prove that the Hardy spaces $H^p(\mathbb{R}^n)$ can be characterized by a fixed Lipschitz function.
We consider a stationary and isotropic spatial point process, whose a realisation is observed within a large window. In order to predict its local intensity, we propose to define the first- and second-order characteristics of a random…
We study the zeros in the complex plane of the partition function for the Ising model coupled to $2d$ quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two…
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…
This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth…
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…
Ab initio calculations based on the Density Functional Theory are used to show that the Debye frequency is a linear function of density to a high accuracy for several elemental solids at pressures (at least) up to 360 GPa. This implies that…
We discuss the physical properties and accuracy of three distinct dynamical (ie, frequency-dependent) kernels for the computation of optical excitations within linear response theory: i) an a priori built kernel inspired by the dressed…