Related papers: Weak expansion properties and a large deviation pr…
We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic…
We study expansive homeomorphisms of a compact metric space $X$ through the lens of the commutative $C^*$-algebra $C(X)$ of continuous complex-valued functions, viewed as observables of the system. We introduce the notion of expansive…
Small set expansion in high dimensional expanders is of great importance, e.g., towards proving cosystolic expansion, local testability of codes and constructions of good quantum codes. In this work we improve upon the state of the art…
The property of exponential dichotomy can be seen as a generalization of the hyperbolicity condition for non autonomous linear finite dimensional systems of ordinary differential equations. In 1978 W.A. Coppel proved that the exponential…
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…
Let $X\subset\mathbb{R}^n$ be a convex closed and semialgebraic set and let $f$ be a polynomial positive on $X$. We prove that there exists an exponent $N\geq 1$, such that for any $\xi\in\mathbb{R}^n$ the function…
We discuss sufficient conditions that guarantee the existence of asymptotic expansions for the Central Limit Theorem for weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like…
The goal of this paper is to prove that on surfaces with asymptotically cusp ends the relative determinant of pairs of Laplace operators is well defined. We consider a surface with cusps (M,g) and a metric h on the surface that is a…
We show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called "Topological Collet-Eckmann". More precisely, we prove a large deviation principle for the distribution of…
This paper generalizes the results of [13] and then provides an interesting example. We construct a family of $W$-like maps $\{W_a\}$ with a turning fixed point having slope $s_1$ on one side and $-s_2$ on the other. Each $W_a$ has an…
We investigate typical properties of nonexpansive mappings on unbounded complete hyperbolic metric spaces. For two families of metrics of uniform convergence on bounded sets, we show that the typical nonexpansive mapping is a Rakotch…
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
The well known concept, to reduce the spatio-temporal dynamics beyond instabilities of trivial states to amplitude modulated patterns, is reviewed from the point of view of a formal perturbation expansion for general dissipative partial…
Expander graphs have been intensively studied in the last four decades. In recent years a high dimensional theory of expanders has emerged, and several variants have been studied. Among them stand out coboundary expansion and topological…
The divergence of perturbative expansions for the vast majority of macroscopic systems, which follows from Dyson's collapse argument, prevents Feynman's diagrammatic technique from being directly used for controllable studies of strongly…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
In [1], it is established that a convergent observer with an infinite gain margin can be designed for a given nonlinear system when a Riemannian metric showing that the system is differentially detectable (i.e., the Lie derivative of the…