Related papers: Correlation and lower bounds of arithmetic express…
In this paper, the well-known method of correlation equations for constructing Gibbs measures is generalized based on the concept of the transition energy field. Using the properties of transition energies, we obtain the system of…
This paper describes a method to compute lower bounds for moments of $\zeta$ and $L$-functions. The method is illustrated in the case of moments of $|\zeta(\frac 12+it)|$, where the results are new for small moments $0< k<1$.
We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small…
We investigate correlation functions in a periodic box-ball system. For the two point functions of short distance, we give explicit formulae obtained by combinatorial methods. We give expressions for general N-point functions in terms of…
We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…
We determine the pair correlations of countable sets $T \subset \mathbb{R}^n$ satisfying natural equidistribution conditions. The pair correlations are computed as the volume of a certain region in $\mathbb{R}^{2n}$, which can be expressed…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
We use Rice's formulas in order to compute the moments of some level functionals which are linked to problems in oceanography and optics. For instance, we consider the number of specular points in one or two dimensions, the number of…
Four point correlation functions for many electrons at finite temperature in periodic lattice are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite…
Extensions of earlier algorithms and enhanced visualization techniques for approximating a correlation matrix are presented. The visualization problems that result from using column or colum--and--row adjusted correlation matrices, which…
We investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a…
Coordination sequences of periodic and quasiperiodic graphs are analysed. These count the number of points that can be reached from a given point of the graph by a number of steps along its bonds, thus generalising the familiar coordination…
We study the molecular correlations in a lattice model of a solution of a low-solubility solute, with emphasis on how the thermodynamics is reflected in the correlation functions. The model is treated in Bethe-Guggenheim approximation,…
We review the basic notion of correlations in point processes, adapted to the language of high energy physicists. The measurement of accessible information on correlations by means of correlation integrals is summarized. Applications to the…
We report on an exact calculation of lattice correlation functions on a finite four-dimensional lattice with either Euclidean or Minkowskian signature. The lattice correlation functions are calculated by the method of differential…
We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative regime. The techniques we consider are integration-by-parts…
We obtain asymptotic formulae with optimal error terms for the number of lattice points under and near a dilation of the standard parabola, the former improving upon an old result of Popov. These results can be regarded as achieving the…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
In this work, we develop Extraction Theorems for classes of geometric objects with small extraction numbers. These classes include intervals, axis-parallel segments, axis-parallel rays, and octants. We investigate these classes of objects…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…