Does a Single Zealot Affect an Infinite Group of Voters ?

Details Does a Single Zealot Affect an Infinite Group of Voters ? Does a Single Zealot Affect an Infinite Group of Voters ?

2003-04-30

arxiv.org/abs/cond-mat/0304670v2

Phys. Rev. Lett. 91, 028701 (2003)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2-column revtex4 format

Scientific paper

10.1103/PhysRevLett.91.028701

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.

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