Related papers: Independent sets of a given size and structure in …

We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As an application, we prove that a set of positive measure in…

Given $n$ independent random vectors with common density $f$ on $\mathbb{R}^d$, we study the weak convergence of three empirical-measure based estimators of the convex $\lambda$-level set $L_\lambda$ of $f$, namely the excess mass set, the…

We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…

A theorem of Shearer states that every $n$-vertex triangle-free graph of maximum degree $d \geq 2$ contains an independent set of size at least $(d\log d - d + 1)/(d - 1)^2 \cdot n$. Ajtai, Koml\'{o}s, Pintz, Spencer and Szemer\'{e}di…

In this note, using methods introduced by Hacon, McKernan and Xu, we study the accumulation points of volumes of varieties of log general type. First, we show that, if the set of boundary coefficients $\Lambda$ is DCC, closed under limits…

We consider three types of multivariate records in this paper and derive the mean and the variance of their numbers for independent and uniform random samples from two prototype regions: hypercubes $[0,1]^d$ and $d$-dimensional simplex.…

This paper presents some finite combinatorics of set systems with applications to model theory, particularly the study of dependent theories. There are two main results. First, we give a way of producing lower bounds on VC_ind-density, and…

The independence density of a finite hypergraph is the probability that a subset of vertices, chosen uniformly at random contains no hyperedges. Independence densities can be generalized to countable hypergraphs using limits. We show that,…

We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if $G$ is a virtually compact special hyperbolic group, and $Q\leq G$ is a $K$-quasiconvex…

Let $ \mathbb{L}^{d} = ( \mathbb{Z}^{d},\mathbb{E}^{d} ) $ be the $ d $-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on $ \mathbb{L}^{d} $ in which every edge inside the $ s $-dimensional…

We prove a multivariate central limit theorem with explicit error bound on a non-smooth function distance for sums of bounded decomposable $d$-dimensional random vectors. The decomposition structure is similar to that of Barbour, Karo\'nski…

We give a generalized and self-contained account of Haglund-Paulin's wallspaces and Sageev's construction of the CAT(0) cube complex dual to a wallspace. We examine criteria on a wallspace leading to finiteness properties of its dual cube…

We study the dynamics of polynomial maps on the boundary of the central hyperbolic component $\mathcal H_d$. We prove the local connectivity of Julia sets and a rigidity theorem for maps on the regular part of $\partial\mathcal H_d$. Our…

We introduce and study a class of discrete particle ensembles that naturally arise in connection with classical random matrix ensembles, log-gases and Jack polynomials. Under technical assumptions on a general analytic potential we prove…

In this paper, we are concerned with multivariate Gegenbauer approximation of functions defined in the $d$-dimensional hypercube. Two new and sharper bounds for the coefficients of multivariate Gegenbauer expansion of analytic functions are…

We calculate the exact analytical coefficients of the $\beta$ expansion of the grand-canonical partition function of the unidimensional Hubbard model up to order $\beta^5$, using an alternative method, based on properties of the Grassmann…

We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For…

We determine the limiting density of the largest sum-free subset of the lattice cube $\{1,2,\ldots,n\}^d$ for all $d$, thus resolving the natural conjecture that it is constructed by two appropriate hyperplane slices.

This paper discusses the asymptotic behaviour of the number of descents in a random signed permutation and its inverse, which was posed as an open problem by Chatterjee and Diaconis in a recent publication. For that purpose, we generalize…

In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic 3-space H^3. Galvez, Martinez and Milan showed that when the singular set does not accumulate at an end, the end is asymptotic to a…