Solution of the Voter Model by Spectral Analysis

Abstract

An exact spectral analysis of the Markov Propagator for the Voter model is presented for the complete graph, and extended to the complete bipartite graph and uncorrelated random networks. Using a well-defined Martingale approximation in diffusion-dominated regions of phase space, which is almost everywhere for the Voter model, this method is applied to compute analytically several key quantities such as exact expressions for the $m$ time step propagator of the Voter model, all moments of consensus times, and the local times for each macrostate. This spectral method is motivated by a related method for solving the Ehrenfest Urn problem and by formulating the Voter model on the complete graph as an Urn model. Comparisons of the analytical results from the spectral method and numerical results from Monte-Carlo simulations are presented to validate the spectral method.

arXiv comment11 Pages, 6 figures

References in corpus (17)

• Statistical physics of social dynamics
• Random graphs with arbitrary degree distributions and their applications
• The spread of epidemic disease on networks
• Voter Model on Heterogeneous Graphs
• Social consensus through the influence of committed minorities
• Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
• Exact Results for Kinetics of Catalytic Reactions
• Analytical Solution of the Voter Model on Disordered Networks
• Coarsening and persistence in the voter model
• Heterogeneous Voter Models
• Solution of voter model dynamics on annealed small-world networks
• In-depth analysis of the Naming Game dynamics: the homogeneous mixing case
• Voter models on weighted networks
• Social Influencing and Associated Random Walk Models: Asymptotic Consensus Times on the Complete Graph
• Voter models with contrarian agents
• Consensus time and conformity in the adaptive voter model
• Voter models with conserved dynamics

Cited by in corpus (4)

• Analysis of the high dimensional naming game with committed minorities
• Solution of the multi-state voter model and application to strong neutrals in the naming game
• Evidence of Herding and Stubbornness in Jury Deliberations
• A Nonlinear Transform for the Diagonalization of the Bernoulli-Laplace Diffusion Model and Orthogonal Polynomials