Balancing conservative and disruptive growth in the voter model

TL;DR

This paper investigates how different growth strategies in a one-dimensional voter model influence the expected number of state changes, highlighting the balance between conservative and disruptive growth in self-organizing systems.

Contribution

It introduces a framework for controlling state-changes in growing voter models by balancing conservative and disruptive growth forces.

Findings

Expected state-changes can be controlled by growth balance.

Conservative growth preserves self-organization.

Disruptive growth undermines self-organization.

Abstract

We are concerned with how the implementation of growth determines the expected number of state-changes in a growing self-organizing process. With this problem in mind, we examine two versions of the voter model on a one-dimensional growing lattice. Our main result asserts that the expected number of state-changes before an absorbing state is found can be controlled by balancing the conservative and disruptive forces of growth. This is because conservative growth preserves the self-organization of the voter model as it searches for an absorbing state, whereas disruptive growth undermines this self-organization. In particular, we focus on controlling the expected number of state-changes as the rate of growth tends to zero or infinity in the limit. These results illustrate how growth can affect the costs of self-organization and so are pertinent to the physics of growing active matter.