Update rules and interevent time distributions: Slow ordering vs. no ordering in the Voter Model

TL;DR

This paper introduces a flexible update methodology for agent-based models that incorporates arbitrary interevent time distributions, revealing slow ordering phenomena in the voter model under certain update rules.

Contribution

It presents a novel approach to update rules based on interevent times, demonstrating their impact on the dynamics of the voter model across different network types.

Findings

System exhibits slow ordering with power-law decay of interfaces.

Mean absorption time may be undefined due to slow dynamics.

Update rules significantly influence the ordering process.

Abstract

We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state of the agent, so that the update becomes part of the dynamical model. As an illustration we consider the voter model in fully-connected, random and scale free networks with an update probability inversely proportional to the persistence, that is, the time since the last event. We find that in the thermodynamic limit, at variance with standard updates, the system orders slowly. The approach to the absorbing state is characterized by a power law decay of the density of interfaces, observing that the mean time to reach the absorbing state might be not well defined.