Related papers: Dual Seminorms, Ergodic Coefficients and Semicontr…
We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…
This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's projective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We…
The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
In order to successfully explore quantum systems which are perturbations of simple models, it is essential to understand the complexity of perturbation bounds. We must ask ourselves: How quantum many-body systems can be artificially…
This paper develops a novel operator theoretic framework to study the contraction properties of Markov semigroups with respect to a general class of Kantorovich semi-distances, which notably includes Wasserstein distances. The rather simple…
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique…
The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction methods, associated to functionally weighted Banach spaces for…
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
The hypercontractivity is proved for the Markov semigroup associated to a class of finite/infinite dimensional stochastic Hamiltonian systems. Consequently, the Markov semigroup is exponentially convergent to the invariant probability…
In this paper the stability and the perturbation bounds of Markov operators acting on abstract state spaces are investigated. Here, an abstract state space is an ordered Banach space where the norm has an additivity property on the cone of…
We develop a novel stability theory for Sinkhorn semigroups based on Lyapunov techniques and quantitative contraction coefficients, and establish exponential convergence of Sinkhorn iterations on weighted Banach spaces. This…
In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship…
Ergodic properties of a stochastic medium complexity model for atmosphere and ocean dynamics are analysed. More specifically, a two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by…