Coarsening in the persistent voter model: Analytical results.

Area of Science:

• Statistical Physics
• Social Dynamics
• Complex Systems

Background:

• The persistent voter model is a key framework for understanding opinion dynamics.
• Real-world social systems often exhibit agents with fixed opinions (zealots).
• Previous models may not fully capture the interplay between opinion change and immutability.

Purpose of the Study:

• To investigate the coarsening dynamics of a simplified persistent voter model incorporating zealots.
• To analyze how agent interactions and the emergence of zealots influence opinion spread.
• To provide a tractable mathematical framework for studying these dynamics.

Main Methods:

• Development of a simplified persistent voter model with zealot agents.
• Derivation of governing equations for one-point and two-point correlation functions.
• Application of approximate closure schemes and analytical solutions.
• Validation through numerical simulations.

Main Results:

• The simplified model successfully captures key features of the original persistent voter model.
• Analytical solutions for correlation functions were obtained.
• The derived equations, though not closed, were effectively managed using approximation schemes.
• Analytical results showed strong agreement with numerical simulations.

Conclusions:

• The simplified persistent voter model with zealots offers a valuable tool for studying opinion dynamics.
• The findings validate the use of approximate closure schemes in complex systems modeling.
• This work provides a foundation for further research into social influence and opinion formation.