Related papers: Fixation to Consensus on Tree-related Graphs
We consider a consensus algorithm in which every node in a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node…
We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a…
We investigate a set of stochastic models of biodiversity, population genetics, language evolution and opinion dynamics on a network within a common framework. Each node has a state, 0 < x_i < 1, with interactions specified by strengths…
The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of…
In this article, we investigate the asymptotic formation of consensus for several classes of time-dependent cooperative graphon dynamics. After motivating the use of this type of macroscopic models to describe multi-agent systems, we adapt…
In this work, we consider a finite-state inhomogeneous-time Markov chain whose probabilities of transition from one state to another tend to decrease over time. This can be seen as a cooling of the dynamics of an underlying Markov chain. We…
Theoretical computer science plays an important role in the understanding of social networks and their properties. We can model information rippling throughout social networks, or the opinions of social media users for example, using graph…
We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of…
Distributed consensus algorithm over networks of quantum systems has been the focus of recent studies in the context of quantum computing and distributed control. Most of the progress in this category have been on the convergence conditions…
In a model of communication in a social network described by a simple consensus model, we pose the problem of finding a subset of nodes with given cardinality and fixed consensus values that enable the fastest convergence rate to…
The property of spatial mixing and strong spatial mixing in spin systems has been of interest because of its implications on uniqueness of Gibbs measures on infinite graphs and efficient approximation of counting problems that are otherwise…
We analyze stability of consensus algorithms in networks of multi-agents with time-varying topologies and delays. The topology and delays are modeled as induced by an adapted process and are rather general, including i.i.d.\ topology…
In this paper we study a discrete time consensus model on a connected graph with monotonically increasing peer-pressure and noise perturbed outputs masking a hidden state. We assume that each agent maintains a constant hidden state and a…
This paper considers synchronous discrete-time dynamical systems on graphs based on the threshold model. It is well known that after a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of…
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).…
In this paper, we prove the first-order convergence law for the uniform attachment random graph with almost all vertices having the same degree. In the considered model, vertices and edges are introduced recursively: at time $m+1$ we start…
We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…
Majority dynamics on the binomial Erd\H{o}s-R\'enyi graph $\mathsf{G}(n,p)$ with $p=\lambda/\sqrt{n}$ is studied. In this process, each vertex has a state in $\{0,1\}$ and at each round, every vertex adopts the state of the majority of its…
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…
We present consensus analysis of systems with single integrator dynamics interacting via time-varying graphs under the event-triggered control paradigm. Event-triggered control sparsifies the control applied, thus reducing the control…