Numerical analysis of the rebellious voter model

TL;DR

This paper provides numerical analysis of the rebellious voter model, a variation of the voter model favoring minority types, revealing phase transitions and exact critical points in related models.

Contribution

It offers numerical data and insights into phase transitions and critical points of the rebellious voter model and its one-sided variant, highlighting unexplained exact formulas.

Findings

Both models show a phase transition between coexistence and noncoexistence.

The one-sided model's critical point appears exactly at 0.5.

Explicit formulas describe key functions of the one-sided model.

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.