Related papers: A remark on the minimal dispersion

We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…

We consider minimal hypersurfaces inside the unit ball whose boundary on the sphere is a small perturbation of the link of a minimizing quadratic cone. We show that such minimal surfaces are uniquely determined by their boundary condition.…

We address several extremal problems concerning the spreading property of point sets of Steiner triple systems. This property is closely related to the structure of subsystems, as a set is spreading if and only if there is no proper…

We consider the problem of lower bounding a generalized Minkowski measure of subsets of a convex body with a log-concave probability measure, conditioned on the set size. A bound is given in terms of diameter and set size, which is sharp…

We establish a general principle that any lower bound on the non-vanishing of central $L$-values obtained through studying the one-level density of low-lying zeros can be refined to show that most such $L$-values have the typical size…

This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…

Let $p_1,\ldots,p_n$ be a set of points in the unit square and let $T_1,\ldots,T_n$ be a set of $\delta$-tubes such that $T_j$ passes through $p_j$. We prove a lower bound for the number of incidences between the points and tubes under a…

We study the probabilistic existence of point configurations satisfying the $(0, m, d)$-net property in base $b$ within a randomly generated point set of size $N$ in the $d$-dimensional unit cube. We first derive an upper bound on the…

We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the…

We prove a lower bound that agrees with Manin's prediction for the number of rational points of bounded height on the Fermat cubic surface. As an application we provide a simple counterexample to Manin's conjecture over the rationals.

In this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed non-regular local rings, bounding them uniformly away from one. Our results improve previous work of Aberbach and Enescu.

We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…

We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of…

We provide a monotone non increasing sequence of upper bounds $f^H_k$ ($k\ge 1$) converging to the global minimum of a polynomial $f$ on simple sets like the unit hypercube. The novelty with respect to the converging sequence of upper…

Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…

Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…

We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability…

We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread are obtained when a given nxn complex…

Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an…

Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…