Related papers: The metric theory of the pair correlation function…

We derive an expression for the correlation function of the random force on a soliton which is consistent with the constraints needed to integrate out the zero modes which appear due to the broken translational symmetry of the soliton…

The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.

Let $\alpha$ be a real number greater than $1$. We establish an effective lower bound for the distance between an integral power of $\alpha$ and its nearest integer.

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…

The partial fraction expansion of coth($\pi$z), due to Euler, is generalized to power series having for coefficients the Riemann zeta function evaluated at certain arithmetic sequences. A further generalization using arbitrary Dirichlet…

We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the…

The fundamental measure density functional theory for hard spheres is generalized to binary mixtures of arbitrary positive and moderate negative non-additivity between unlike components. In bulk the theory predicts fluid-fluid phase…

This paper explores large sample properties of the two-parameter $(\alpha,\theta)$ Poisson--Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure, viewing this process as a natural extension…

We study the distribution of spacings between squares modulo q, where q is square-free and highly composite, in the limit as the number of prime factors of q goes to infinity. We show that all correlation functions are Poissonian, which…

A method for the calculation of translationally invariant wave functions for systems of identical fermions with arbitrary potential of pair interaction is developed. It is based on the well-known result that the essential dynamic part of…

This is a review of several results related to distribution of powers and combination of powers modulo 1. We include a proof that given a sequence of real numbers $\theta_n$, it is possible to get an $\alpha$ (given $\lambda \ne 0$), or a…

We consider the ratio of the correlation function of n+1 local operators over the correlator of the first n of these operators in planar N=4 super-Yang-Mills theory, and consider the limit where the first n operators become pairwise null…

In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…

Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values…

Pair densities and associated correlation functions provide a critical tool for introducing many-body correlations into a wide-range of effective theories. Ab initio calculations show that two-nucleon pair-densities exhibit strong spin and…

We consider the partial theta function $\theta (q,z):=\sum _{j=0}^{\infty}q^{j(j+1)/2}z^j$, where $(q,z)\in \mathbb{C}^2$, $|q|<1$. We show that for any $0<\delta _0<\delta <1$, there exists $n_0\in \mathbb{N}$ such that for any $q$ with…

Particle pair-correlations are broadly used to describe particle distributions in chemistry, physics, and material science. Many theoretical methods require the pair-correlation to predict material properties such as fluid flow, thermal…

We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2.

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general…

We study the correlations of pairs of complex logarithms of $\mathbb Z$-lattice points in the complex line at various scalings, proving the existence of pair correlation functions. We prove that at the linear scaling, the pair correlations…