Does a Single Zealot Affect an Infinite Group of Voters ?
Abstract
A method for studying exact properties of a class of 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 ( t-1/2) in 1d and much slower ( 1/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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