Related papers: Beginning of stability theory for Polish Spaces
We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: for every $\theta$ there is a dependent theory $T$ of size $\theta$ such that for all $\kappa$ and $\delta$,…
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…
Quasi-Polish spaces were introduced by de Brecht as a possibly non-Hausdorff generalization of Polish spaces sharing many of their descriptive set-theoretic properties. We give a self-contained exposition of the basic theory of quasi-Polish…
We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.
Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the…
We consider the problem of global stability of solutions to a class of semilinear wave equations with null condition in Minkowski space. We give sufficient conditions on the given solution which guarantees stability. Our stability result…
Several uncertainty principles are proved for the Fock space.
We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of…
Let $\mathcal A$ and $\mathcal B$ be two closed linear relation acting between two Banach spaces $X$ and $Y$ and let $\lambda$ be a complex number. We study the stability of the nullity and deficiency of $\mathcal A$ when it is perturbed by…
In this paper, we present preliminary results on the stability of massless particles in two and three-planet systems. The results of our study may be used to address questions concerning the stability of terrestrial planets in these systems…
We show that the ample degree of a stable theory with trivial forking is preserved when we consider the corresponding theory of belles paires, if it exists. This result also applies to the theory of $H$-structures of a trivial theory of…
This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…
By using the notion of a Haar ambivalent set introduced by Balka, Buczolich and Elekes (2012), essentially new classes of statistical structures having objective and strong objective estimates of unknown parameters are introduced in a…
The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
A new proof of Friedrich's theorem on the existence and stability of asymptotically de Sitter spaces in 3+1 dimensions is given, which extends to all even dimensions. In addition, we characterize the possible limits of spaces which are…
Given a compact space in a fixed universe of set theory, one can naturally define its interpretation in any ZFC extension of the universe. We investigate the stability of some classes of compact spaces with respect to extensions of this…
We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.
The stability of topological persistence is one of the fundamental issues in topological data analysis. Numerous methods have been proposed to address the stability of persistent modules or persistence diagrams. Recently, the concept of…
In this article, we establish necessary and sufficient viability conditions for continuity inclusions over the 1-Wasserstein space. Depending on the regularity properties of the dynamics, we derive two results which are based on fairly…