Related papers: Remarks on Tao's algebraic regularity lemma

We prove a structure theorem for stable functions on amenable groups, which extends the arithmetic regularity lemma for stable subsets of finite groups. Given a group $G$, a function $f\colon G\to [-1,1]$ is called stable if the binary…

We prove trace estimates for the relativistic $\alpha$-stable process extending the result of Ba\~{n}uelos and Kulczycki (2008) in the stable case.

The aim of this paper is to generalize and improve two of the main model-theoretic results of "Stable group theory and approximate subgroups" by E. Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence…

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…

A Thomas-Fermi-Weizsaecker type theory is constructed, by means of which we are able to give a relatively simple proof of the stability of relativistic matter. Our procedure has the advantage over previous ones in that the critical value of…

At present, there exists no physically plausible example of a quantum field theory for which the existence of solutions has been proven mathematically. The Clay Mathematics Institute has offered a prize for proving existence for a class of…

The conditions for stability of the elements of linear groups over the associative rings with identity and their connection with the stability of rings are analyzed in the article. The stability of rings which are commutative, satisfy the…

In the paper we have developed a theory of stability preserving structural transformations of systems of second-order ordinary differential equations (ODEs), i.e., the transformations which preserve the property of Lyapunov stability. The…

We set up a generalization of ubiquitous one-parameter families in algebraic geometry and their use for stability theories ([GIT, HL, AHLH]) to families over toric varieties and their analytic analogues. The language allows us to…

We classify the stable formulas in the theory of Dense Linear Orders without endpoints, the stable formulas in the theory of Divisible Abelian Groups, and the stable formulas without parameters in the theory of Real Closed Fields. The third…

We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…

In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.

Homological stability has shown itself to be a powerful tool for the computation of homology of families of groups such as general linear groups, mapping class groups or automorphisms of free groups. We survey here tools and techniques for…

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of a Cauchy-Jensen additive functional equation in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated…

We prove an asymptotic saturation-type version of Rota's basis conjecture. It relies on the connection of Tao's slice rank with unstable tensors from geometric invariant theory.

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

We study a stability property of probability laws with respect to small violations of algorithmic randomness. A sufficient condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like…

Regularity theorems \`a la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random elliptic operators have been available for a while, on general…

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…

We prove a stability version of the Pr\'ekopa-Leindler inequality.