Does a Single Zealot Affect an Infinite Group of Voters ?

Abstract

A method for studying exact properties of a class of {\it inhomogeneous} stochastic many-body systems is developed and presented in the framework of a voter model perturbed by the presence of a ``zealot'', an individual allowed to favour an opinion. We compute exactly the magnetization of this model and find that in one (1d) and two dimensions (2d) it evolves, algebraically ($\sim t^{-1/2}$) in 1d and much slower ($\sim 1/\ln t$) in 2d, towards the unanimity state chosen by the zealot. In higher dimensions the stationary magnetization is no longer uniform: the zealot cannot influence all the individuals. Implications to other physical problems are also pointed out.

arXiv comment4 pages, 2-column revtex4 format

References in corpus (9)

• Theory of Phase Ordering Kinetics
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Exact Results for Kinetics of Catalytic Reactions
• Coarsening and persistence in the voter model
• Freezing and Slow Evolution in a Constrained Opinion Dynamics Model
• Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains
• Exact Calculation of the Spatio-temporal Correlations in the Takayasu model and in the q-model of Force Fluctuations in Bead Packs
• Impurity in a Granular Fluid
• Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction

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