Related papers: Differentiation of sets - The general case
The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a…
For a compact convex subset K with non-empty interior in a finite-dimensional vector space, let G be the group of all smooth diffeomorphisms of K which fix the boundary of K pointwise. We show that G is a C^0-regular infinite-dimensional…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
This paper studies the K-theory of categories of partially cancellative monoid sets, which is better behaved than that of all finitely generated monoid sets. A number of foundational results are proved, making use of the formalism of…
Two of the authors have defined the class $ WDC(M)$ as the class of all subsets of a smooth manifold $M$ that may be expressed in local coordinates as certain sublevel sets of DC (differences of convex) functions. If $M$ is Riemanian and…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
First we develop the theory of local rules for coboundary categories. Then we describe the local rules in two main cases. First for the quantum groups in general and in the seminormal representations of the Hecke algebras. Then for crystals…
In this paper, we investigate the combinatorial structure and asymptotic distribution of the solution set of the equation $\sigma(n+1) = k\sigma(n)$ for a given integer $k>1$. From a combinatorial perspective, the solutions to this equation…
We provide a refined combinatorial identity for the set of partitions of $\{1,\dots, n\}$, which plays an important role in investigating several limit theorems related to finite free convolutions. Firstly, we present the finite free…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…
Our work builds on known results for k-uniform hypergraphs including the existence of limits, a Regularity Lemma and a Removal Lemma. Our main tool here is a theory of measures on ultraproduct spaces which establishes a correspondence…
We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to…
We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa\la and Weso\lowski (Statist. Probab.…
We investigate continuous parameter dependence for solutions of general boundary value problems for ordinary linear differential systems. The generalization of Kiguradze's theorem (1987) on correctness of such problems was obtained. Also…
In this paper we introduce and study the so-called continuous $K$-theory for a certain class of "large" stable $\infty$-categories, more precisely, for dualizable presentable categories. For compactly generated categories, the continuous…
We deduce a generalized hydrodynamic limit for the box-ball system, which explains how the densities of solitons of different sizes evolve asymptotically under Euler space-time scaling. To describe the limiting soliton flow, we introduce a…
We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality…
We consider large random matrices $X$ with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical…
We study an extended dynamical system on the non-negative real line with piecewise linear non-uniformly expanding local dynamics. With a uniformly distributed initial state, the distribution of successive states coincides with that of a…