Related papers: Solution-free sets for sums of binary forms

In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…

We prove an analogue of the Oppenheim conjecture for a system comprising an inhomogeneous quadratic form and a linear form in $3$ variables using dynamics on the space of affine lattices.

We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…

In this paper we give some two-dimensional and some three-dimensional examples for the shape of the symmetric solution set of a linear complementarity problem where the given data are not explicitly known but can only be enclosed in…

We examine the lattice generated by two pairs of supplementary vector subspaces of a finite-dimensional vector space by intersection and sum, with the aim of applying the results to the study of representations admitting two pairs of…

We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of…

We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…

The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…

We investigate the number of symmetric matrices of non-negative integers with zero diagonal such that each row sum is the same. Equivalently, these are zero diagonal symmetric contingency tables with uniform margins, or loop-free regular…

The density of the hyperbolic metric on the complement of a rectangular lattice is investigated. The question is related to conformal mapping of symmetric circular quadrilaterals with all zero angles.

We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…

We obtain estimates for Vinogradov's integral which for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's…

We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of…

Let A be a finite set of integers. For a polynomial f(x_1,...,x_n) with integer coefficients, let f(A) = {f(a_1,...,a_n) : a_1,...,a_n \in A}. In this paper it is proved that for every pair of normalized binary linear forms f(x,y)=u_1x+v_1y…

The large N limit of mean spectral density for the ensemble of NxN sub-unitary matrices derived by Wei and Fyodorov (J. Phys. A: Math. Theor. 41 (2008) 50201) is calculated by a modification of the saddle point method. It is shown that the…

We prove that every indefinite quadratic form with non-negative integer coefficients is the volume polynomial of a pair of lattice polygons. This solves the discrete version of the Heine-Shephard problem for two bodies in the plane. As an…

In this note, we prove a central limit theorem for smooth linear statistics of zeros of random polynomials which are linear combinations of orthogonal polynomials with iid standard complex Gaussian coefficients. Along the way, we obtain…

Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two…

We consider systems of stochastic fixed-point equations that arise in the asymptotic analysis of random recursive structures and algorithms such as Quicksort, generalized P\'olya urn processes and path lengths of random recursive trees and…

We calculate numerically the density of states n(S) for SU(2) lattice gauge theory on $L^4$ lattices. Small volume dependence are resolved for small values of S. We compare $ln(n(S))$ with weak and strong coupling expansions. Intermediate…