Related papers: Spectral gap and stability for groups and non-loca…
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative estimate showing that if the spectral gap of an RCD$(N-1,…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
We study stability of metric approximations of countable groups with respect to groups endowed with ultrametrics, the main case study being a $p$-adic analogue of Ulam stability, where we take $GL_n(\mathbb{Z}_p)$ as approximating groups…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
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,…
The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these…
We consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique…
Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…
The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…
Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…
A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that…
We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…
We prove the spectral gap property for random walks on the product of two non-locally isomorphic analytic real or p-adic compact groups with simple Lie algebras, under the necessary condition that the marginals posses a spectral gap.…
New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…
The stable roommates problem is a non-bipartite version of the stable matching problem in a bipartite graph. In this paper, we consider the stable roommates problem with ties. In particular, we focus on strong stability, which is one of the…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints.…
Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner, the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterized in…
We analyze the stability and stabilizability properties of mixed retarded-neutral type systems when the neutral term is allowed to be singular. Considering an operator model of the system in a Hilbert space we are interesting in the…