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Related papers: Groups with arbitrarily poor permutation stability

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A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…

Operator Algebras · Mathematics 2021-04-21 Søren Eilers , Tatiana Shulman , Adam P. W. Sørensen

This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…

Quantum Physics · Physics 2015-06-04 Ian R. Petersen , Valery Ugrinovskii , Matthew R. James

In this paper we consider Tyler's robust covariance M-estimator under group symmetry constraints. We assume that the covariance matrix is invariant to the conjugation action of a unitary matrix group, referred to as group symmetry. Examples…

Applications · Statistics 2015-09-30 Ilya Soloveychik , Dmitry Trushin , Ami Wiesel

The second author introduced notions of weak permutability and commutativity between groups and proved the finiteness of a group generated by two weakly permutable finite groups. Two groups H,K weakly commute provided there exists a…

Group Theory · Mathematics 2009-06-29 Ricardo N. Oliveira , Said N. Sidki

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…

Group Theory · Mathematics 2017-10-20 Martin R. Bridson , David M. Evans , Martin W. Liebeck , Dan Segal

Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on…

Computer Science and Game Theory · Computer Science 2024-08-20 Kimon Boehmer , Niclas Boehmer

Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…

Statistics Theory · Mathematics 2026-01-21 Abhinav Chakraborty , Yuetian Luo , Rina Foygel Barber

We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…

Group Theory · Mathematics 2018-03-15 S. P. Glasby , Cheryl E. Praeger , Kyle Rosa , Gabriel Verret

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This…

Group Theory · Mathematics 2023-09-20 Anton A. Baykalov , Alice Devillers , Cheryl E. Praeger

A new approach to superstability and finite time extinction of strongly continuous semigroups is presented, unifying known results and providing new criteria for these conditions to hold analogous to the well-known Pazy condition for…

Functional Analysis · Mathematics 2013-09-26 D. Creutz , M. Mazo , C. Preda

We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are HS-stable. We investigate the permanence of HS-stability…

Group Theory · Mathematics 2023-07-19 Caleb Eckhardt , Tatiana Shulman

We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…

Numerical Analysis · Mathematics 2024-03-25 Erik Burman , Mihai Nechita , Lauri Oksanen

In this paper we consider the {\em conjugacy stability} property of subgroups and provide effective procedures to solve the problem in several classes of groups. In particular, we start with free groups, that is, we give an effective…

Group Theory · Mathematics 2021-07-14 Isabel Fernández Martínez , Denis Serbin

We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…

Quantum Physics · Physics 2015-06-11 Vladimir V. Kornyak

We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…

Group Theory · Mathematics 2007-05-23 Alexandre V. Borovik , Alexei G. Myasnikov , Vladimir Shpilrain

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…

Dynamical Systems · Mathematics 2020-01-28 Yair Hartman , Bryna Kra , Scott Schmieding

A finite non-regular primitive permutation group $G$ is extremely primitive if a point stabiliser acts primitively on each of its nontrivial orbits. Such groups have been studied for almost a century, finding various applications. The…

Combinatorics · Mathematics 2022-11-07 Melissa Lee , Gabriel Verret

The stability analysis of possibly time varying positive semigroups on non necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety…

Probability · Mathematics 2023-04-18 Marc Arnaudon , Pierre Del Moral , El Maati Ouhabaz

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…

Optimization and Control · Mathematics 2022-01-06 Darinka Dentcheva , Yang Lin , Spiridon Penev

Let $G$ be a transitive permutation group on a finite set of size at least $2$. By a well known theorem of Fein, Kantor and Schacher, $G$ contains a derangement of prime power order. In this paper, we study the finite primitive permutation…

Group Theory · Mathematics 2015-10-19 Timothy C. Burness , Hung P. Tong-Viet