相关论文: The Asynchronous DeGroot Dynamics
The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free…
In the deterministic binary majority process we are given a simple graph where each node has one out of two initial opinions. In every round, every node adopts the majority opinion among its neighbors. By using a potential argument first…
We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its…
It is widely believed that society is becoming increasingly polarized around important issues, a dynamic that does not align with common mathematical models of opinion formation in social networks. In particular, measures of polarization…
We describe a protocol for the average consensus problem on any fixed undirected graph whose convergence time scales linearly in the total number nodes $n$. The protocol is completely distributed, with the exception of requiring all nodes…
We consider the limiting behavior of the count of subgraphs isomorphic to a graph $G$ with $m\geq 0$ fixed endpoints (or roots) in the random-connection model, as the intensity $\lambda$ of the underlying Poisson point process tends to…
In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local…
In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph.…
Opinion dynamics is of paramount importance as it provides insights into the complex dynamics of opinion propagation and social relationship adjustment. It is assumed in most of the previous works that social relationships evolve much…
Can classical consensus models predict the group behavior of large language models (LLMs)? We examine multi-round interactions among LLM agents through the DeGroot framework, where agents exchange text-based messages over diverse…
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 introduce a DeGroot-based model for opinion dynamics in social networks. A community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. The model is formalized using labeled…
We introduce a simple dynamic model of opinion formation, in which a finite population of individuals hold vector-valued opinions. At each time step, each individual's opinion moves towards the mean opinion but is then perturbed…
We study the evolution of opinions on a directed network with community structure. Individuals update their opinions synchronously based on a weighted average of their neighbors' opinions, their own previous opinions, and external media…
We generalize the asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model to a wide class of random graphs. Among others, this class contains the Poissonian random graph, the expected degree…
We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or…
Concentration inequalities for subgraph counts in random geometric graphs built over Poisson point processes are proved. The estimates give upper bounds for the probabilities $\mathbb{P}(N\geq M +r)$ and $\mathbb{P}(N\leq M - r)$ where $M$…
We address discrete-time consensus on the Euclidean unit sphere. For this purpose we consider a distributed algorithm comprising the iterative projection of a conical combination of neighboring states. Neighborhoods are represented by a…
We consider an asynchronous voting process on graphs which we call discordant voting, and which can be described as follows. Initially each vertex holds one of two opinions, red or blue say. Neighbouring vertices with different opinions…
We perform a thorough study of various characteristics of the asynchronous push-pull protocol for spreading a rumor on Erd\H{o}s-R\'enyi random graphs $G_{n,p}$, for any $p>c\ln(n)/n$ with $c>1$. In particular, we provide a simple strategy…