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Numerical Analysis of the Rebellious Voter Model

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Abstract

The rebellious voter model, introduced by Sturm and Swart (2008), is a variation of the standard, one-dimensional voter model, in which types that are locally in the minority have an advantage. It is related, both through duality and through the evolution of its interfaces, to a system of branching annihilating random walks that is believed to belong to the ‘parity-conservation’ universality class. This paper presents numerical data for the rebellious voter model and for a closely related one-sided version of the model. Both models appear to exhibit a phase transition between noncoexistence and coexistence as the advantage for minority types is increased. For the one-sided model (but not for the original, two-sided rebellious voter model), it appears that the critical point is exactly a half and two important functions of the process are given by simple, explicit formulas, a fact for which we have no explanation.

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Correspondence to Jan M. Swart.

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Swart, J.M., Vrbenský, K. Numerical Analysis of the Rebellious Voter Model. J Stat Phys 140, 873–899 (2010). https://doi.org/10.1007/s10955-010-0021-x

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