Related papers: Uniformly global observables for 1D maps with an i…

In this paper we showed that under two assumptions we are able to define interesting functions that we call generalized local coefficients. We showed that in the quasi-split case generalized local coefficients are up to a positive constant…

Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they…

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of…

The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between finite-dimensional and infinite-dimensional spaces. We first…

In infinite ergodic theory, two distributional limit theorems are well-known. One is characterized by the Mittag-Leffler distribution for time averages of $L^1(m)$ functions, i.e., integrable functions with respect to an infinite invariant…

For non-uniformly expanding maps inducing with a general return time to Gibbs Markov maps, we provide sufficient conditions for obtaining higher order asymptotics for the correlation function in the infinite measure setting. Along the way,…

Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to…

We study random circle maps that are expanding on the average. Uniform bounds on neither expansion nor distortion are required. We construct a coupling scheme, which leads to exponential convergence of measures (memory loss) and exponential…

In his recent research M. K. Tam (2018) considered a framework for the analysis of iterative algorithms which can be described in terms of a structured set-valued operator. At each point in the ambient space, the value of the operator can…

For a countable abelian group $G$ we investigate generic properties of the space of all invariant metrics on $G$. We prove that for every such an unbounded group $G$, i.e. group which has elements of arbitrarily high order, there is a dense…

We extend the notion of localic completion of generalised metric spaces by Steven Vickers to the setting of generalised uniform spaces. A generalised uniform space (gus) is a set X equipped with a family of generalised metrics on X, where a…

Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…

Lidskii's additive inequalities (both for eigenvalues and singular values) can be interpreted as an explicit description of global minimizers of functions that are built on unitarily invariant norms, with domains consisting of certain…

Kochen-Specker theorems assure the breakdown of certain types of non-contextual hidden variable theories through the non-existence of global, holistic frame functions; alas they do not allow us to identify where this breakdown occurs, nor…

We demonstrate when and how an entire left-infinite orbit of an underlying dynamical system or observations from such left-infinite orbits can be uniquely represented by a pair of elements in a different space, a phenomenon which we call…

We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M. Heins, we also show that there is a universal bounded locally univalent function on the unit disk.…

Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…

We consider two classes of piecewise expanding maps $T$ of $[0,1]$: a class of uniformly expanding maps for which the Perron-Frobenius operator has a spectral gap in the space of bounded variation functions, and a class of expanding maps…

We consider exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the…

Let $(X,G)$, $(Y,G)$ be two $G$-systems, where $G$ is an infinite countable discrete amenable group and $X$, $Y$ are compact metric spaces. Suppose that $\mathcal{U}$ is a cover of $X$. We first introduce the conditional local topological…