Anomalous diffusion in nonlinear transformations of the noisy voter model

TL;DR

This paper investigates anomalous diffusion phenomena in nonlinear transformations of the noisy voter model, revealing various diffusion regimes through analytical and numerical methods.

Contribution

It introduces a novel perspective by analyzing the noisy voter model through nonlinear transformations to uncover different diffusion behaviors.

Findings

Original voter model exhibits ballistic diffusion.

Nonlinear transformations reveal multiple diffusion regimes.

Numerical simulations match analytical approximations.

Abstract

Voter models are well known in the interdisciplinary community, yet they haven't been studied from the perspective of anomalous diffusion. In this paper we show that the original voter model exhibits ballistic regime. Non-linear transformations of the observation variable and time scale allows us to observe other regimes of anomalous diffusion as well as normal diffusion. We show that numerical simulation results coincide with derived analytical approximations describing the temporal evolution of the raw moments.