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 welldefined Martingale approximation in diffusiondominated 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 timestep 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.
 Publication:

Physical Review E
 Pub Date:
 January 2015
 DOI:
 10.1103/PhysRevE.91.012812
 arXiv:
 arXiv:1408.2130
 Bibcode:
 2015PhRvE..91a2812P
 Keywords:

 02.50.Le;
 87.23.Ge;
 02.50.Ga;
 05.40.Fb;
 Decision theory and game theory;
 Dynamics of social systems;
 Markov processes;
 Random walks and Levy flights;
 Mathematics  Probability;
 Condensed Matter  Statistical Mechanics;
 Physics  Physics and Society
 EPrint:
 11 Pages, 6 figures