Related papers: Fixation to Consensus on Tree-related Graphs
Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for…
In this paper, we study the consensus problem for continuous-time and discrete-time multi-agent systems in state-dependent switching networks. In each case, we first consider the networks with fixed connectivity, in which the communication…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
In this letter, we study the problem of accelerating reaching average consensus over connected graphs in a discrete-time communication setting. Literature has shown that consensus algorithms can be accelerated by increasing the graph…
We consider a linear consensus system with n agents that can switch between r different connectivity patterns. A natural question is which switching law yields the best (or worst) possible speed of convergence to consensus? We formulate…
In the standard nearest-neighbor coarsening model with state space $\{-1,+1\}^{\mathbb{Z}^2}$ and initial state chosen from symmetric product measure, it is known (see~\cite{NNS}) that almost surely, every vertex flips infinitely often. In…
Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…
We establish necessary and sufficient conditions for consistent root reconstruction in continuous-time Markov models with countable state space on bounded-height trees. Here a root state estimator is said to be consistent if the probability…
We prove an apparently novel concentration of measure result for Markov tree processes. The bound we derive reduces to the known bounds for Markov processes when the tree is a chain, thus strictly generalizing the known Markov process…
This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…
We consider Markovian dynamics on a typical realization of the so-called Directed Configuration Model (DCM), that is, a random directed graph with prescribed in- and out-degrees. In this random geometry, we study the meeting time of two…
We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of…
We address the problem of determining if a discrete time switched consensus system converges for any switching sequence and that of determining if it converges for at least one switching sequence. For these two problems, we provide…
In this paper, we study the consensus problem for networked dynamic systems with arbitrary initial states, and present some structural characterization and direct construction of consensus functions. For the consensus problem under similar…
We consider a system of $N$ particles interacting through their empirical distribution on a finite state space in continuous time. In the formal limit as $N\to\infty$, the system takes the form of a nonlinear (McKean--Vlasov) Markov chain.…
We consider the convergence time for solving the binary consensus problem using the interval consensus algorithm proposed by B\' en\' ezit, Thiran and Vetterli (2009). In the binary consensus problem, each node initially holds one of two…
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using Transportation Cost Inequalities for stochastic…
We study the local convergence of critical Galton-Watson trees and Levy trees under various conditionings. Assuming a very general monotonicity property on the functional of random trees, we show that random trees conditioned to have large…
We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…
We study the state consensus problem for linear shift-invariant discrete-time homogeneous multi-agent systems (MASs) over time-varying graphs. A novel approach based on the small gain theorem is proposed to design the consensus control…