Related papers: Uniform approximation of continuous couplings

The critical behavior for intermittency is studied in two coupled one-dimensional (1D) maps. We find two fixed maps of an approximate renormalization operator in the space of coupled maps. Each fixed map has a common relavant eigenvaule…

Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…

A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…

The aim of the note is to extend the uniformization theorem to compact Kahler spaces X with mild singularities and establish a kind of rigidity of their universal coverings. We assume the fundamental group of X is large, residually finite…

We study solutions to conformally invariant equations with isolated singularties.

The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…

In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed…

Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…

We derive the non-asymptotical non-uniform sharp error estimation for Bernstein's approximation of continuous function based on the modern probabilistic apparatus. We investigate also the convergence of derivative of these polynomials and…

We study statistical properties of the k-nearest neighbors algorithm for multiclass classification, with a focus on settings where the number of classes may be large and/or classes may be highly imbalanced. In particular, we consider a…

We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…

We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…

This paper is about quantitative linearization results for the Monge-Amp\`ere equation with rough data. We develop a large-scale regularity theory and prove that if a measure $\mu$ is close to the Lebesgue measure in Wasserstein distance at…

The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this…

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit…

Two Bayesian models with different sampling densities are said to be marginally equivalent if the joint distribution of observables and the parameter of interest is the same for both models. We discuss marginal equivalence in the general…

In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements,…

We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show…

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…