Jornal article

Swart J., Vrbenský K.

Journal of Statistical Physics

140

2010

5 (2010)

873-899

0022-4715

Ing. Karel Vrbenský (ÚTIA - Oddělení stochastické informatiky)

rebellious voter model, parity conservation, exactly solvabl

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.