Solution of the voter model by spectral analysis

William Pickering and Chjan Lim
Phys. Rev. E 91, 012812 – Published 16 January 2015

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 19 September 2014

DOI:https://doi.org/10.1103/PhysRevE.91.012812

©2015 American Physical Society

Authors & Affiliations

William Pickering and Chjan Lim

  • Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 91, Iss. 1 — January 2015

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×