Global culture: A noise induced transition in finite systems

TL;DR

This paper studies how cultural noise influences the stability of cultural diversity in Axelrod's model, revealing a noise-induced transition between multicultural and monocultural states in finite systems.

Contribution

It provides a rigorous analysis of noise effects in Axelrod's model, demonstrating a transition mechanism based on relaxation times and noise rates.

Findings

Disordered multicultural states are metastable.

Noise rate below 1/T leads to monoculture.

In the thermodynamic limit, disorder persists despite local convergence.

Abstract

We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural configurations are found to be metastable. This general result is proven rigorously in d=1, where the dynamics is described in terms of a Lyapunov potential. In d=2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r < 1/T induces monocultural configurations, whereas r > 1/T sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.