Noisy voter model: Explicit expressions for finite system size

Area of Science:

• Statistical Physics
• Complex Systems Modeling

Background:

• Urn models are foundational stochastic processes for complex systems.
• Voter and Ehrenfest models are prominent examples of urn models.

Purpose of the Study:

• To introduce and analyze a novel opinion model merging voter and Ehrenfest dynamics.
• To investigate the behavior of a noisy voter model with a tunable noise parameter (α).

Main Methods:

• Spectral analysis to derive analytical expressions.
• Utilizing dual Hahn polynomials for distribution calculations.
• Investigating power-law distributions and their exponents.

Main Results:

• Explicit formulas for order parameter, susceptibility, and Binder's cumulant.
• Recursive expressions for first passage and return distributions.
• Identification of a system-size-dependent pseudocritical noise value.

Conclusions:

• The combined model provides a framework for understanding noisy opinion dynamics.
• Analytical tools allow for precise characterization of system behavior.
• The concept of pseudocritical noise is relevant for finite-size systems.