Related papers: Consensus in non-commutative spaces
This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
For piecewise monotone interval maps we look at Birkhoff spectra for regular potential functions. This means considering the Hausdorff dimension of the set of points for which the Birkhoff average of the potential takes a fixed value. In…
In this note we give sufficient conditions for the convergence of the iterative algorithm called weighted-average consensus in directed graphs. We study the discrete-time form of this algorithm. We use standard techniques from matrix theory…
We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence…
In this article, we generalize the definition of the probabilistic Gel'fand width from the Hilbert space to the strictly convex reflexive space by giving Birkhoff left orthogonal decomposition theorem. Meanwhile, a more natural definition…
We use the Hilbert distance on cones and the Birkhoff-Hopf Theorem to prove decay of correlation, analyticity of the free energy and a central limit theorem in the one dimensional Jellium model with non constant density charge background,…
A new theorem on conditions for convergence to consensus of a multiagent time-dependent time-discrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to results by Moreau (IEEE…
Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…
A theorem on (partial) convergence to consensus of multiagent systems is presented. It is proven with tools studying the convergence properties of products of row stochastic matrices with positive diagonals which are infinite to the left.…
The Robbins-Siegmund theorem is one of the most important results in stochastic optimization, where it is widely used to prove the convergence of stochastic algorithms. We provide a quantitative version of the theorem, establishing a bound…
We show that for almost every map in a transversal one-parameter family of piecewise expanding unimodal maps the Birkhoff sum of suitable observables along the forward orbit of the turning point satisfies the law of iterated logarithm. This…
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…
We analyze the consensus based optimization method proposed by Pinnau et al.(2017) in one dimension. We rigorously provide a quantitative error estimate between the consensus point and global minimizer of a given objective function. Our…
This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…
Convergence properties of time inhomogeneous Markov chain based discrete and continuous time linear consensus algorithms are analyzed. Provided that a so-called infinite jet flow property is satisfied by the underlying chains, necessary…
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries).…
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…