Related papers: Generic Stability and Modes of Convergence
We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
We study non-orthogonality of symmetric, regular types and show that it preserves generic stability and is an equivalence relation on the set of all generically stable, regular types. We will also prove that some of the nice properties from…
In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that…
In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…
Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…
Concentration of measure is studied, and obtained, for stable and related random vectors.
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
Tests of the stability of nature's fundamental constants are one of the cornerstones of the ongoing search for the new physics which is required to explain the recent acceleration of the universe. The two main settings for these tests are…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
We develop a theory of generically stable and smooth Keisler measures in NIP metric theories, generalizing the case of classical logic. Using smooth extensions, we verify that fundamental properties of (Borel)-definable measures and the…
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
Extensively evaluating the capabilities of (large) language models is difficult. Rapid development of state-of-the-art models induce benchmark saturation, while creating more challenging datasets is labor-intensive. Inspired by the recent…
We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of…
In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of "generic stability" in arbitrary theories. Among other things, we show that the standard definition of generic…