Related papers: Discordant edges for the voter model on regular ra…
The voter model is a classical interacting particle system explaining consensus formation on a social network. Real social networks feature not only a heterogeneous degree distribution but also connections changing over time. We study the…
The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions…
We consider the plurality consensus problem among $n$ agents. Initially, each agent has one of $k$ different opinions. Agents choose random interaction partners and revise their state according to a fixed transition function, depending on…
For a one-dimensional simple symmetric random walk $(S_n)$, an edge $x$ (between points $x-1$ and $x$) is called a favorite edge at time $n$ if its local time at $n$ achieves the maximum among all edges. In this paper, we show that with…
This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These…
Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry breaking transition was reported [M. Lallouache et al, Phys. Rev. E, {\bf 82} 056112 (2010)]. We generalise the model to…
We consider 3-Majority, a probabilistic consensus dynamics on a complete graph with $n$ vertices, each vertex starting with one of $k$ initial opinions. At each discrete time step, a vertex $u$ is chosen uniformly at random. The selected…
We generalize a binary majority-vote model on adaptive networks to its plurality-vote counterpart and analyze the time scale to consensus when voters are given more than two options. When opinions are uniformly distributed in the population…
We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter $k \ge 0$, in addition to its $+$ or $-$ opinion state. The evolution of the…
When it comes to the mathematical modelling of social interaction patterns, a number of different models have emerged and been studied over the last decade, in which individuals randomly interact on the basis of an underlying graph…
In the consensus model of Krause-Hegselmann, opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. A randomly chosen agent takes…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
In this paper we investigate the problem of the sudden disconnection of an edge in a discrete-time multi-agent consensus network. If the graph remains strongly connected, the multi-agent system still achieves consensus, but in general,…
Public opinion is often affected by the presence of committed groups of individuals dedicated to competing points of view. Using a model of pairwise social influence, we study how the presence of such groups within social networks affects…
We study opinion dynamics in a population of interacting adaptive agents voting on a set of complex multidimensional issues. We consider agents which can classify issues into for or against. The agents arrive at the opinions about each…
A recent line of work studies models of opinion exchange where agent opinions about $d$ topics are tracked simultaneously. The opinions are represented as vectors on the unit $(d-1)$-sphere, and the update rule is based on the overall…
We study opinion evolution in networks of stubborn agents discussing a sequence of issues, modeled through the so called concatenated Friedkin-Johnsen (FJ) model. It is concatenated in the sense that agents' opinions evolve for each issue,…
Polarization is a well-documented phenomenon across a wide range of social issues. However, prevailing theories often compartmentalize the examination of herding behavior and opinion convergence within different contexts. In this study, we…
The frog model with a Bernoulli initial configuration is an interacting particle system on the $d$-dimensional lattice ($d \geq 2$) with two types of particles: active and sleeping. Active particles perform independent simple random walks.…
We study the scaling limit of a large class of voter model perturbations in one dimension, including stochastic Potts models, to a universal limiting object, the continuum voter model perturbation. The perturbations can be described in…