Related papers: Generic stability and stability

In this article, we discuss stability of the one-dimensional overdamped Lange\-vin equation in double-well potential. We determine unstable and stable equilibria, and discuss the rate of convergence to stable ones. Also, we derive…

The mean ergodic theorem is equivalent to the assertion that for every function K and every epsilon, there is an n with the property that the ergodic averages A_m f are stable to within epsilon on the interval [n,K(n)]. We show that even…

We consider principal bundles as generalized morphisms between topological groupoids. In the category of these generalized morphisms two topological groupoids are isomorphic if and only if they are Morita equivalent. We show that the fibers…

The celebrated result of Gortler-Healy-Thurston (independently, Jackson-Jord\'an for $d=2$) shows that the global rigidity of graphs realised in the $d$-dimensional Euclidean space is a generic property. Extending this result to the global…

This paper has been withdrawn by the authors due to an error in the proof of Lemma 3.9. The correct proof of global stability is given in arXiv:1101.5177

Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such…

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

Let $N$ be a normal subgroup of a group $G$. An $N$-module $Q$ is $G$-stable provided that $Q$ is equivalent to the twist $Q^g$ of $Q$ by $g$, for every $g\in G$. If the action of $N$ on $Q$ extends to an action of $G$ on $Q$, $Q$ is…

We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets,…

The Navier-Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any $L^2$-perturbation. In particular the general hypothesis…

In this paper, we present a new argument (see Lemma 3.4) that allows us to simplify the proof of stability of peakons established in Lin and Liu (2009) (Theorem 1.1).

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…

In these notes we give a shortened and more direct proof of Goto's generalized Kaehler stability theorem stating that if (J_1,J_2) is a generalized kaehler structure for which J_2 is determined by a nowhere vanishing closed form, then small…

In this paper, we prove a $p$-Hardy inequality on the discrete half-line with weights $n^{\alpha}$ for all real $p > 1$. Building on the work of Miclo for $p = 2$ and Muckenhoupt in the continuous settings, we develop a quantitative…

A theorem of Waldspurger states that the Fourier transform of a stable distribution on the Lie algebra of a simply-connected semisimple group $G$ over a p-adic field, is again stable. We generalize this theorem to representations whose…

We prove a statement concerning hyperlinearity for central extensions of property (T) groups in the presence of flexible HS-stability, and more generally, weak ucp-stability. Notably, this result is applied to show that if $\text{Sp}_{2g}…

In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…

We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…

This is the second of two papers treating faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties; in the first paper we considered the module itself and its projective space, while…

We prove a dichotomy for $D$-rank 1 types in simple theories that generalizes Buechler's dichotomy for $D$-rank 1 minimal types in stable theories: every $D$-rank 1 type is either 1-based or part of its algebraic closure, defined by a…