Related papers: Stable normed algebras
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
We study several different notions of algebraicity in use in stable homotopy theory and prove implications between them. The relationships between the different meanings of algebraic are unexpectedly subtle, and we illustrate this with…
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…
As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix…
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…
We introduce stabilised property Gamma, a C*-algebraic variant of property Gamma which is invariant under stable isomorphism. We then show that simple separable nuclear C*-algebras with stabilised property Gamma and $\mathrm{Cu}(A) \cong…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
We introduce a relaxation of stability, called almost sure stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a non-standard finite group. We show that almost sure stability satisfies a stationarity principle…
We investigate a family of distributions having a property of stability-under-addition, provided that the number $\nu$ of added-up random variables in the random sum is also a random variable. We call the corresponding property a…
In this paper, we introduce the concept of stable automorphic forms for semisimple algebraic groups and use the stability of automorphic forms to study the geometry of infinite dimensional arithmetic quotients.
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…
In this paper we study stable finiteness of ample groupoid algebras with applications to inverse semigroup algebras and Leavitt path algebras, recovering old results and proving some new ones. In addition, we develop a theory of (faithful)…
We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.
We prove that the faithful and uniqueness of norm properties are stable in different product algebras such as direct-sum product algebra, convolution product algebra, and module product algebra. Further, we exhibit that these properties are…
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
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…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.
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…
Recently, bipath persistent homology has been proposed as an extension of standard persistent homology, along with its visualization (bipath persistence diagram) and computational methods. In the setting of standard persistent homology, the…